Tugas Anum.xlsx
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GAUSS JORDAN x1 x2 0 8 3 5 6 2
3 0 6
5 8 2
x3 2 2 8
c -7 8 26
2 2 8
8 -7 26
iterasi 1
1 0 0
1.6666667 0.6666667 2.6666667 8 2 -7 -8 4 10
iterasi 2
1 0 0
0 1 0
0.25 0.25 6
4.125 -0.875 3
iterasi 3
1 0 0
0 1 0
0 0 1
4 -1 0.5
a11 a21 a31
a12 a22 a32
a13 a23 a33
3 0 6
[A] 5 8 2
2 2 8
L11 L21 L31
3 0 6
U12 U13 U23
1.6666667 0.6666667 0.25
gauss s
gauss jacobi
iterasi
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
3 0 6
5 8 2
2 2 8
x1 0 2.6666667 1.9583333 4.5 3.2682292 4.9192708 3.4321289 4.7457682 3.3933004 4.5969543 3.4256789 4.5253805 3.4903961 4.4750019 3.5491664
x2 0 -0.875 -1.6875 -1.242188 -1.425781 -0.921387 -1.163818 -0.822723 -1.116714 -0.849089 -1.121051 -0.878639 -1.115251 -0.893906 -1.102754
x3 0 3.25 1.46875 2.203125 0.1855469 1.1552734 -0.209106 0.9668579 -0.103645 0.9842033 0.0145564 0.9610035 0.0756244 0.9110156 0.1172251
8 -7 26
3 0 6
iterasi
1 2 3 4 5 6 7 8 9 10 11 12 13 14
x1 0 2.6666667 3.1458333 3.9361979 4.2310384 4.1498973 4.0121177 3.9599733 3.9736982 3.9977136 4.0069332 4.0046144 4.000429 3.9987993 3.9991905
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
4.4264397 3.597968 4.3807578 3.6405946 4.3398113 3.6788476 4.303458 3.7131608 4.2710553 3.7438223 4.2421058 3.7711953 4.2162401 3.7956393 4.1931365 3.8174721 4.172502 3.8369729 4.1540724 3.8543904 4.1376117 3.869947 4.1229096 3.8838415 4.1097782 3.8962516 4.0980498 3.9073358 4.0875744 3.9172359 4.0782181 3.9260782 4.0698615 3.9339758 4.0623977 3.9410297 4.0557312 3.9473299 4.0497771 3.9529571 4.044459 3.957983 4.0397091 3.962472 4.0354667 3.9664814 4.0316775
-0.904306 -1.090953 -0.914062 -1.081066 -0.923237 -1.072455 -0.931488 -1.064745 -0.93882 -1.057829 -0.945353 -1.051648 -0.95119 -1.046129 -0.956404 -1.041201 -0.961062 -1.036799 -0.965222 -1.032868 -0.968938 -1.029356 -0.972256 -1.02622 -0.97522 -1.023418 -0.977868 -1.020916 -0.980232 -1.018682 -0.982344 -1.016686 -0.984231 -1.014903 -0.985915 -1.013311 -0.98742 -1.011889 -0.988764 -1.010619 -0.989965 -1.009484 -0.991037 -1.008471 -0.991994 -1.007566 -0.99285
0.8638136 0.1562468 0.8242623 0.192947 0.7898204 0.2259507 0.758978 0.2552784 0.7313155 0.2814135 0.7065905 0.304759 0.6845154 0.3256174 0.6648028 0.3442487 0.6471961 0.360889 0.6314701 0.3757513 0.6174241 0.3890257 0.6048788 0.4008819 0.5936738 0.4114715 0.5836659 0.4209296 0.5747272 0.4293773 0.5667436 0.4369225 0.5596128 0.4436615 0.5532439 0.4496806 0.5475555 0.4550566 0.5424748 0.4598583 0.5379369 0.4641469 0.5338838 0.4679774 0.5302637 0.4713986 0.5270304
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
3.9999199 4.0002079 4.000142 4.0000149 3.999964 3.9999751 3.9999972 4.0000062 4.0000044 4.0000005 3.9999989 3.9999992 4 4 4 4 4 4 4 4 4 4 4 4 4
62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
3.9700625 4.0282932 3.9732609 4.0252704 3.9761177 4.0225706 3.9786692 4.0201592 3.9809481 4.0180054 3.9829836 4.0160818 3.9848016 4.0143636 3.9864253 4.012829 3.9878756 4.0114584 3.989171 4.0102342 3.9903279 4.0091408 3.9913613 4.0081642 3.9922842 4.007292 3.9931085 4.0065129 3.9938448 4.0058171 3.9945024 4.0051956 3.9950898 4.0046405 3.9956144 4.0041448 3.9960829 4.0037019 3.9965014 4.0033064 3.9968752 4.0029532 3.997209 4.0026377 3.9975072 4.0023559 3.9977735
-1.006758 -0.993614 -1.006036 -0.994296 -1.005391 -0.994905 -1.004815 -0.99545 -1.0043 -0.995936 -1.003841 -0.99637 -1.003431 -0.996758 -1.003064 -0.997104 -1.002737 -0.997414 -1.002444 -0.99769 -1.002183 -0.997937 -1.00195 -0.998157 -1.001742 -0.998354 -1.001556 -0.99853 -1.001389 -0.998687 -1.001241 -0.998827 -1.001108 -0.998953 -1.00099 -0.999064 -1.000884 -0.999164 -1.00079 -0.999254 -1.000705 -0.999333 -1.00063 -0.999405 -1.000563 -0.999468 -1.000503
0.4744543 0.5241426 0.4771835 0.5215632 0.4796212 0.5192595 0.4817984 0.5172018 0.483743 0.515364 0.4854799 0.5137226 0.4870312 0.5122565 0.4884167 0.510947 0.4896543 0.5097775 0.4907596 0.5087329 0.4917468 0.5077999 0.4926286 0.5069666 0.4934161 0.5062223 0.4941195 0.5055575 0.4947478 0.5049637 0.4953089 0.5044334 0.4958101 0.5039598 0.4962577 0.5035367 0.4966575 0.5031589 0.4970146 0.5028214 0.4973336 0.5025199 0.4976185 0.5022507 0.4978729 0.5020103 0.4981002
109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155
4.0021042 3.9980114 4.0018794 3.9982239 4.0016786 3.9984136 4.0014992 3.9985831 4.0013391 3.9987345 4.001196 3.9988697 4.0010682 3.9989904 4.0009541 3.9990983 4.0008522 3.9991946 4.0007611 3.9992807 4.0006798 3.9993575 4.0006072 3.9994262 4.0005423 3.9994875 4.0004844 3.9995422 4.0004326 3.9995911 4.0003864 3.9996348 4.0003451 3.9996738 4.0003082 3.9997087 4.0002753 3.9997398 4.0002459 3.9997676 4.0002196 3.9997924 4.0001962 3.9998146 4.0001752 3.9998344 4.0001565
-0.999525 -1.000449 -0.999576 -1.000401 -0.999621 -1.000358 -0.999662 -1.00032 -0.999698 -1.000286 -0.99973 -1.000255 -0.999759 -1.000228 -0.999785 -1.000204 -0.999808 -1.000182 -0.999828 -1.000162 -0.999847 -1.000145 -0.999863 -1.00013 -0.999878 -1.000116 -0.999891 -1.000103 -0.999902 -1.000092 -0.999913 -1.000082 -0.999922 -1.000074 -0.99993 -1.000066 -0.999938 -1.000059 -0.999944 -1.000052 -0.99995 -1.000047 -0.999956 -1.000042 -0.99996 -1.000037 -0.999965
0.5017955 0.4983031 0.5016037 0.4984844 0.5014323 0.4986463 0.5012793 0.498791 0.5011426 0.4989201 0.5010206 0.4990355 0.5009115 0.4991385 0.5008141 0.4992306 0.5007272 0.4993128 0.5006495 0.4993862 0.5005801 0.4994518 0.5005181 0.4995104 0.5004628 0.4995627 0.5004133 0.4996094 0.5003692 0.4996511 0.5003297 0.4996884 0.5002945 0.4997217 0.500263 0.4997514 0.5002349 0.499778 0.5002098 0.4998017 0.5001874 0.4998229 0.5001674 0.4998418 0.5001495 0.4998587 0.5001335
156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202
3.9998521 4.0001398 3.9998679 4.0001248 3.999882 4.0001115 3.9998946 4.0000996 3.9999059 4.0000889 3.9999159 4.0000794 3.9999249 4.000071 3.9999329 4.0000634 3.9999401 4.0000566 3.9999465 4.0000506 3.9999522 4.0000452 3.9999573 4.0000403 3.9999619 4.000036 3.999966 4.0000322 3.9999696 4.0000287 3.9999728 4.0000257 3.9999757 4.0000229 3.9999783 4.0000205 3.9999806 4.0000183 3.9999827 4.0000163 3.9999846 4.0000146 3.9999862 4.000013 3.9999877 4.0000116 3.999989
-1.000033 -0.999968 -1.00003 -0.999972 -1.000027 -0.999975 -1.000024 -0.999978 -1.000021 -0.99998 -1.000019 -0.999982 -1.000017 -0.999984 -1.000015 -0.999986 -1.000014 -0.999987 -1.000012 -0.999989 -1.000011 -0.99999 -1.00001 -0.999991 -1.000009 -0.999992 -1.000008 -0.999993 -1.000007 -0.999994 -1.000006 -0.999994 -1.000005 -0.999995 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.4998738 0.5001193 0.4998873 0.5001065 0.4998993 0.5000951 0.4999101 0.500085 0.4999197 0.5000759 0.4999283 0.5000678 0.4999359 0.5000605 0.4999428 0.5000541 0.4999489 0.5000483 0.4999544 0.5000431 0.4999592 0.5000385 0.4999636 0.5000344 0.4999675 0.5000307 0.499971 0.5000275 0.4999741 0.5000245 0.4999768 0.5000219 0.4999793 0.5000196 0.4999815 0.5000175 0.4999835 0.5000156 0.4999853 0.5000139 0.4999868 0.5000124 0.4999882 0.5000111 0.4999895 0.5000099 0.4999906
203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249
4.0000104 3.9999902 4.0000093 3.9999912 4.0000083 3.9999922 4.0000074 3.999993 4.0000066 3.9999937 4.0000059 3.9999944 4.0000053 3.999995 4.0000047 3.9999955 4.0000042 3.999996 4.0000038 3.9999964 4.0000034 3.9999968 4.000003 3.9999972 4.0000027 3.9999975 4.0000024 3.9999977 4.0000021 3.999998 4.0000019 3.9999982 4.0000017 3.9999984 4.0000015 3.9999986 4.0000014 3.9999987 4.0000012 3.9999989 4.0000011 3.999999 4.000001 3.9999991 4.0000009 3.9999992 4.0000008
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.5000089 0.4999916 0.5000079 0.4999925 0.5000071 0.4999933 0.5000063 0.499994 0.5000056 0.4999947 0.500005 0.4999952 0.5000045 0.4999957 0.500004 0.4999962 0.5000036 0.4999966 0.5000032 0.499997 0.5000029 0.4999973 0.5000026 0.4999976 0.5000023 0.4999978 0.500002 0.4999981 0.5000018 0.4999983 0.5000016 0.4999985 0.5000015 0.4999986 0.5000013 0.4999988 0.5000012 0.4999989 0.500001 0.499999 0.5000009 0.4999991 0.5000008 0.4999992 0.5000007 0.4999993 0.5000007
250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283
3.9999993 4.0000007 3.9999993 4.0000006 3.9999994 4.0000006 3.9999995 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.4999994 0.5000006 0.4999994 0.5000005 0.4999995 0.5000005 0.4999996 0.5000004 0.4999996 0.5000004 0.4999996 0.5000003 0.4999997 0.5000003 0.4999997 0.5000003 0.4999997 0.5000002 0.4999998 0.5000002 0.4999998 0.5000002 0.4999998 0.5000002 0.4999998 0.5000002 0.4999999 0.5000001 0.4999999 0.5000001 0.4999999 0.5000001 0.4999999 0.5000001
L11 L21 L31
CROUT 0 L22 L32
3 0 6
[L] 0 8 -8
L22 L32
8 -8
0 0 L33
0 0 6
1 0 0
1 0 0
L33
U12 1 0
U13 U23 1
[U] 1.6666667 0.6666667 1 0.25 0 1
6
3 0 6
[L] 0 8 -8
y11 y21 y31
2.6666667 -0.875 0.5
1 0 0
x11 x21 x31
gauss seidel 5 8 2
2 2 8
x2 0 -0.875 -1.242188 -1.175293 -1.022919 -0.958113 -0.969276 -0.995808 -1.007243 -1.005384 -1.000765 -0.998748 -0.999057 -0.999861 -1.000216
x3 0 1.46875 1.2011719 0.5916748 0.3324509 0.3771052 0.4832308 0.5289719 0.5215371 0.5030609 0.4949914 0.4962261 0.4994424 0.5008657 0.5006612
8 -7 26
0 0 6
[U] 1.6666667 0.6666667 1 0.25 0 1
4 -1 0.5
-1.000165 -1.000025 -0.999963 -0.999971 -1 -1.000006 -1.000005 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.5001014 0.4998504 0.4998842 0.4999816 0.5000258 0.5000203 0.5000033 0.4999955 0.4999964 0.4999994 0.5000008 0.5000006 0.5000001 0.4999999 0.4999999 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
[Y] 2.6666667 -0.875 0.5
[X] 4 -1 0.5
=
=
[B] 8 -7 26
[Y] 2.6666667 -0.875 0.5
GAUSS JACOBI 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 1 0 0 0 -1
0 0 0 1000 0 0
1 0 0 0 0 0 va
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 1 0 0
0 0 0.6 1 1.6 -0.8
0 0 iterasi 0 1 0 iterasi 1 0 0 iterasi 2 0 -1666.66666667 iterasi 3 0 -1333.33333333 iterasi 4 -1 0 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
0 -1 0 0 0 0
ha 0 0 0 0 1000 -666.667 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56 iterasi 57 iterasi 58 iterasi 59 iterasi 60 iterasi 61 iterasi 62 iterasi 63 iterasi 64 iterasi 65 iterasi 66 iterasi 67 iterasi 68 iterasi 69 iterasi 70 iterasi 71 iterasi 72 iterasi 73 iterasi 74 iterasi 75 iterasi 76 iterasi 77 iterasi 78 iterasi 79 iterasi 80 iterasi 81 iterasi 82
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iterasi 83 iterasi 84 iterasi 85 iterasi 86 iterasi 87 iterasi 88 iterasi 89 iterasi 90 iterasi 91 iterasi 92 iterasi 93 iterasi 94 iterasi 95 iterasi 96 iterasi 97 iterasi 98 iterasi 99 iterasi 100
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 1 0 0
vb
s1 0 0 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 -1666.67 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
0 0 0.6 1 1 0 s2 0 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
0 1 0 0 0 -1
0 0 0 -1666.67 -833.333 -666.667
1 0 0 0 0 0
s3 0 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
iterasi 0 iterasi 1 iterasi 2 iterasi 3 iterasi 4 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
0 0 1000 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
gauss seidel 0 -1 0 0 0 0
0 0 1 0 0 0
0
0
0 -666.6666667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.6 0.8 0 1 0 0
0 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 0 0.6 1 1 0
0 0 -1666.67 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333
0 1 0 0 0 -1
0 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
0 0 0 -1666.67 -833.333 -666.667
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
-833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333
666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
va 1 0 0 0 0 0
ha 0 0 0 1 0 0
vb 0 0 -1 0 0 0
s1 -0.6 -0.8 0 0 0.6 0.8
s2 0 0 0.6 -0.8 0.8 -0.6
s3 0 1 -1 0 0 0
=
1 = masukin angka minus 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
0 0 0 1000
0
0
0
-0.8
0.8
0
0
0
0
0
0
-0.8
-1
0
GAUSS JORDAN iterasi 1
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 1 0 0 0 -1
0 0 0 1000 0 0
iterasi 2
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0.6 -0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 -1 0 0 0 -1
0 0 0 1000 0 0
iterasi 3
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0.6 -0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 -1 0 0 0 -1
0 0 0 1000 0 0
iterasi 4
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
-0.6 0.8 0.6 1 1.6 -0.8
0 -1 0 0 0 -1
1000 -1333.333 0 -1666.667 -1333.333 0
iterasi 5
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 -1 0 0 0 -1
500 -666.6667 500 -833.3333 -833.3333 -666.6667
iterasi 6
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
500 0 500 -833.3333 -833.3333 666.66667
c 0 0 0 0 20 0
CROUT [A] 1 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
1 0 0 0
0 -1 0 0
0
0
0
-0.8
0.8
0
0
0
0
0
0
0
-0.8
-1
0
0
L11 L21 L31 L41 L51 L61
1 0 0 0 0 0
L22 L32 L42 L52 L62
-1 0 0 0 0
L33 L43 L53 L63
u12 u13 u14 u15 u16
0 0 0.6 0 0
u23 u24 u25 u26
0 -0.8 0 -1
u34 u35 u36
[L] 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 -0.6 -0.8 0
0 0 0 0 1.6 -0.8
0 0 0 0 0 -1
0.6 -0.8 0 1 0 0
0 0 0.6 1 1 0
0 -1 0 0 0 1
[U] 1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
[L]^-1 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 -1.666667 -0.833333 0.6666667
0 0 0 0 0.625 -0.5
0 0 0 0 0 -1
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
-0.6 0.8 0 1 0 0
0.6 -0.8 -0.6 -1 1 0
0 1 0 0 0 1
[L]
[U]
0 0 1 0
0 0 0 -0.6
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0.6 -0.8 0 1
0 0 0.6 1
0 -1 0 0
0
-0.8
1.6
0
0
0
0
0
1
0
0
0
-0.8
-1
0
0
0
0
0
1
1 0 0 0
L44 L54 L64
-0.6 -0.8 0
L55 L65
1.6 -0.8
L66
-1
0 0.6 0
u45 u46
1 0
u56
0
[Y] 0 0 0 -1666.667 0 0
[B] 0 0 0 1000 0 0
y11 y21 y31 y41 y51 y61
0 0 0 -1666.667 0 0
[Y] 0 0 0 -1666.667 0 0
x11 x21 x31 x41 x51 x61
va ha hc s1 s2 s3
[X] 1000 0 0 -1666.667 0 0
=
1000 0 0 -1666.667 0 0
L 0 0 0 1000 0 0
0 0 0 -1666.667 -833.3333 666.66667
#N/A #N/A #N/A #N/A #N/A #N/A
0 0 0 -1666.667 -833.3333 666.66667
500 1.137E-13 500 -833.3333 -833.3333 666.66667
U
X
Y
DOOLITTLE A
L
1 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0
0
0
-0.8
0.8
0
0
0
0
0
0
0
0
-0.8
-1
0
0
0
U11
1
U12 U22
0 -1
U13 U23 U33
0 0 1
U14 U24 U34 U44
0.6 0.8 0 -0.6
L21 L31 L41 L51 L61
0 0 0 0 0
L32 L42 L52 L62
0 0 0 0
L43 L53 L63
0 0 0
L54 L64
1.3333333 0
=
0 0 0 0 0 1
[Y] y11 y21 y31 y41 y51 y61
=
0 1 0 0 0 -1
[X] x11 x21 x31 x41 x51 x61
[L] 1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 1.3333333 0
0 0 0 0 1 -0.5
[U] 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 -0.6 0 0
0 0 0.6 -0.6 1.6 0
DOOLITTLE L
U 0 0 0 1
0 0 0 0
0 0 0 0
1 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
1.3333333
1
0
0
0
0
0
1.6
0
0
-0.5
1
0
0
0
0
0
-1
U15 U25 U35 U45 U55
0 0 0.6 -0.6 1.6
U16 U26 U36 U46 U56 U66
0 1 0 0 0 -1
[Y] [Y]
= =
[B] [L]^-1
[B]
[L]
L65
[B] 0 0 0 1000 0 0 [Y] 0 0 0 1000 -1333.333 -666.6667
-0.5
[L]^-1 1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 -1.333333 -0.666667
0 0 0 0 1 0.5
=
0 0 0 0 0 1
[B] 0 0 0 1000 0 0
=
0 -1 0 0 0 -1
[Y] 0 0 0 1000 -1333.333 -666.6667
[U]^-1 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
1 -1.333333 0 -1.666667 0 0
0.375 -0.5 -0.375 -0.625 0.625 0
[Y] 0 0 0 1000 -1333.333 -666.6667 [X] 500 2.274E-13 500 -833.3333 -833.3333 666.66667
GAUSS JACOBI
soal tugas 1 0 0 0 0 0
0 1 0 0 0 0
va iterasi 0 iterasi 1 iterasi 2 iterasi 3 iterasi 4 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.8 -0.6 0.8 0.6 0 0
0 0 -0.6 0.8 0.6 -0.8
1 0 0 0 -1 0
0 0 0 0 0 1
ha
vb
s1
s2
s3
0 0 0 5625 5625 2460.938 2460.938 4240.723 4240.723 3239.594 3239.594 3802.729 3802.729 3485.965 3485.965 3664.145 3664.145 3563.919 3563.919 3620.296 3620.296 3588.584 3588.584 3606.422 3606.422 3596.388 3596.388 3602.032 3602.032 3598.857 3598.857 3600.643 3600.643 3599.638 3599.638 3600.203
0 0 9375 9375 4101.563 4101.563 7067.871 7067.871 5399.323 5399.323 6337.881 6337.881 5809.942 5809.942 6106.908 6106.908 5939.864 5939.864 6033.826 6033.826 5980.973 5980.973 6010.703 6010.703 5993.98 5993.98 6003.386 6003.386 5998.095 5998.095 6001.071 6001.071 5999.397 5999.397 6000.339 6000.339
0 12500 12500 5468.75 5468.75 9423.828 9423.828 7199.097 7199.097 8450.508 8450.508 7746.589 7746.589 8142.544 8142.544 7919.819 7919.819 8045.102 8045.102 7974.63 7974.63 8014.27 8014.27 7991.973 7991.973 8004.515 8004.515 7997.46 7997.46 8001.429 8001.429 7999.196 7999.196 8000.452 8000.452 7999.746
0 0 7500 7500 3281.25 3281.25 5654.297 5654.297 4319.458 4319.458 5070.305 5070.305 4647.954 4647.954 4885.526 4885.526 4751.892 4751.892 4827.061 4827.061 4784.778 4784.778 4808.562 4808.562 4795.184 4795.184 4802.709 4802.709 4798.476 4798.476 4800.857 4800.857 4799.518 4799.518 4800.271 4800.271
0 0 10000 10000 4375 4375 7539.063 7539.063 5759.277 5759.277 6760.406 6760.406 6197.271 6197.271 6514.035 6514.035 6335.855 6335.855 6436.081 6436.081 6379.704 6379.704 6411.416 6411.416 6393.578 6393.578 6403.612 6403.612 6397.968 6397.968 6401.143 6401.143 6399.357 6399.357 6400.362 6400.362
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56 iterasi 57 iterasi 58 iterasi 59 iterasi 60 iterasi 61 iterasi 62 iterasi 63 iterasi 64 iterasi 65 iterasi 66 iterasi 67 iterasi 68 iterasi 69 iterasi 70 iterasi 71 iterasi 72 iterasi 73 iterasi 74 iterasi 75 iterasi 76 iterasi 77 iterasi 78 iterasi 79 iterasi 80 iterasi 81 iterasi 82
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3600.203 3599.886 3599.886 3600.064 3600.064 3599.964 3599.964 3600.02 3600.02 3599.989 3599.989 3600.006 3600.006 3599.996 3599.996 3600.002 3600.002 3599.999 3599.999 3600.001 3600.001 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600
5999.809 5999.809 6000.107 6000.107 5999.94 5999.94 6000.034 6000.034 5999.981 5999.981 6000.011 6000.011 5999.994 5999.994 6000.003 6000.003 5999.998 5999.998 6000.001 6000.001 5999.999 5999.999 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000
7999.746 8000.143 8000.143 7999.92 7999.92 8000.045 8000.045 7999.975 7999.975 8000.014 8000.014 7999.992 7999.992 8000.005 8000.005 7999.997 7999.997 8000.001 8000.001 7999.999 7999.999 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000
4799.847 4799.847 4800.086 4800.086 4799.952 4799.952 4800.027 4800.027 4799.985 4799.985 4800.009 4800.009 4799.995 4799.995 4800.003 4800.003 4799.998 4799.998 4800.001 4800.001 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800
6399.797 6399.797 6400.114 6400.114 6399.936 6399.936 6400.036 6400.036 6399.98 6399.98 6400.011 6400.011 6399.994 6399.994 6400.004 6400.004 6399.998 6399.998 6400.001 6400.001 6399.999 6399.999 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400
iterasi 83 iterasi 84 iterasi 85 iterasi 86 iterasi 87 iterasi 88 iterasi 89 iterasi 90 iterasi 91 iterasi 92 iterasi 93 iterasi 94 iterasi 95 iterasi 96 iterasi 97 iterasi 98 iterasi 99 iterasi 100
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600
6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000
8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000
4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800
6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400
CONTOH SOAL TUGAS TERDAHULU 0 0 0 10000 0 0
iterasi 0 iterasi 1 iterasi 2 iterasi 3 iterasi 4 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
1 0 0 0 0 0
0 1 0 0 0 0
-0.8 -0.6 0.8 0.6 0 0
0 0 -0.6 0.8 0.6 -0.8
1 0 0 0 -1 0
0
0
0
0
0 -7500 4218.75 -2373.05 1334.839 -750.847 422.3514 -237.573 133.6346 -75.1695 42.28283 -23.7841 13.37855 -7.52543 4.233057 -2.38109 1.339366 -0.75339 0.423784 -0.23838 0.134088 -0.07542 0.042426 -0.02386 0.013424 -0.00755 0.004247 -0.00239 0.001344 -0.00076 0.000425 -0.00024 0.000135 -7.57E-05 4.26E-05
0 0 5625 2460.9375 4240.722656 3239.593506 3802.728653 3485.965133 3664.144613 3563.918655 3620.295756 3588.583637 3606.421704 3596.387791 3602.031867 3598.857075 3600.642896 3599.638371 3600.203416 3599.885578 3600.064362 3599.963796 3600.020365 3599.988545 3600.006443 3599.996376 3600.002039 3599.998853 3600.000645 3599.999637 3600.000204 3599.999885 3600.000065 3599.999964 3600.00002
0 9375 4101.563 7067.871 5399.323 6337.881 5809.942 6106.908 5939.864 6033.826 5980.973 6010.703 5993.98 6003.386 5998.095 6001.071 5999.397 6000.339 5999.809 6000.107 5999.94 6000.034 5999.981 6000.011 5999.994 6000.003 5999.998 6000.001 5999.999 6000 6000 6000 6000 6000 6000
0 12500 5468.75 9423.828 7199.097 8450.508 7746.589 8142.544 7919.819 8045.102 7974.63 8014.27 7991.973 8004.515 7997.46 8001.429 7999.196 8000.452 7999.746 8000.143 7999.92 8000.045 7999.975 8000.014 7999.992 8000.005 7999.997 8000.001 7999.999 8000 8000 8000 8000 8000 8000 8000
7500 3281.25 5654.296875 4319.458008 5070.304871 4647.95351 4885.52615 4751.89154 4827.061009 4784.778183 4808.562272 4795.183722 4802.709156 4798.476099 4800.857194 4799.517828 4800.271222 4799.847438 4800.085816 4799.951728 4800.027153 4799.984727 4800.008591 4799.995167 4800.002718 4799.998471 4800.00086 4799.999516 4800.000272 4799.999847 4800.000086 4799.999952 4800.000027 4799.999985 4800.000009
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56
-2.39E-05 1.35E-05 -7.58E-06 4.26E-06 -2.4E-06 1.35E-06 -7.59E-07 4.27E-07 -2.4E-07 1.35E-07 -7.59E-08 4.27E-08 -2.4E-08 1.35E-08 -7.6E-09 4.28E-09 -2.41E-09 1.35E-09 -7.62E-10 4.29E-10 -2.42E-10
3599.999989 3600.000006 3599.999996 3600.000002 3599.999999 3600.000001 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600
6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000
8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000
4799.999995 4800.000003 4799.999998 4800.000001 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800
0 0 0 0 0 1
0 10000 4375 7539.063 5759.277 6760.406 6197.271 6514.035 6335.855 6436.081 6379.704 6411.416 6393.578 6403.612 6397.968 6401.143 6399.357 6400.362 6399.797 6400.114 6399.936 6400.036 6399.98 6400.011 6399.994 6400.004 6399.998 6400.001 6399.999 6400 6400 6400 6400 6400 6400 6400
0 0 0 10000 0 0
6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400
3 0 6
5 8 2
x3 2 2 8
c -7 8 26
2 2 8
8 -7 26
iterasi 1
1 0 0
1.6666667 0.6666667 2.6666667 8 2 -7 -8 4 10
iterasi 2
1 0 0
0 1 0
0.25 0.25 6
4.125 -0.875 3
iterasi 3
1 0 0
0 1 0
0 0 1
4 -1 0.5
a11 a21 a31
a12 a22 a32
a13 a23 a33
3 0 6
[A] 5 8 2
2 2 8
L11 L21 L31
3 0 6
U12 U13 U23
1.6666667 0.6666667 0.25
gauss s
gauss jacobi
iterasi
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
3 0 6
5 8 2
2 2 8
x1 0 2.6666667 1.9583333 4.5 3.2682292 4.9192708 3.4321289 4.7457682 3.3933004 4.5969543 3.4256789 4.5253805 3.4903961 4.4750019 3.5491664
x2 0 -0.875 -1.6875 -1.242188 -1.425781 -0.921387 -1.163818 -0.822723 -1.116714 -0.849089 -1.121051 -0.878639 -1.115251 -0.893906 -1.102754
x3 0 3.25 1.46875 2.203125 0.1855469 1.1552734 -0.209106 0.9668579 -0.103645 0.9842033 0.0145564 0.9610035 0.0756244 0.9110156 0.1172251
8 -7 26
3 0 6
iterasi
1 2 3 4 5 6 7 8 9 10 11 12 13 14
x1 0 2.6666667 3.1458333 3.9361979 4.2310384 4.1498973 4.0121177 3.9599733 3.9736982 3.9977136 4.0069332 4.0046144 4.000429 3.9987993 3.9991905
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
4.4264397 3.597968 4.3807578 3.6405946 4.3398113 3.6788476 4.303458 3.7131608 4.2710553 3.7438223 4.2421058 3.7711953 4.2162401 3.7956393 4.1931365 3.8174721 4.172502 3.8369729 4.1540724 3.8543904 4.1376117 3.869947 4.1229096 3.8838415 4.1097782 3.8962516 4.0980498 3.9073358 4.0875744 3.9172359 4.0782181 3.9260782 4.0698615 3.9339758 4.0623977 3.9410297 4.0557312 3.9473299 4.0497771 3.9529571 4.044459 3.957983 4.0397091 3.962472 4.0354667 3.9664814 4.0316775
-0.904306 -1.090953 -0.914062 -1.081066 -0.923237 -1.072455 -0.931488 -1.064745 -0.93882 -1.057829 -0.945353 -1.051648 -0.95119 -1.046129 -0.956404 -1.041201 -0.961062 -1.036799 -0.965222 -1.032868 -0.968938 -1.029356 -0.972256 -1.02622 -0.97522 -1.023418 -0.977868 -1.020916 -0.980232 -1.018682 -0.982344 -1.016686 -0.984231 -1.014903 -0.985915 -1.013311 -0.98742 -1.011889 -0.988764 -1.010619 -0.989965 -1.009484 -0.991037 -1.008471 -0.991994 -1.007566 -0.99285
0.8638136 0.1562468 0.8242623 0.192947 0.7898204 0.2259507 0.758978 0.2552784 0.7313155 0.2814135 0.7065905 0.304759 0.6845154 0.3256174 0.6648028 0.3442487 0.6471961 0.360889 0.6314701 0.3757513 0.6174241 0.3890257 0.6048788 0.4008819 0.5936738 0.4114715 0.5836659 0.4209296 0.5747272 0.4293773 0.5667436 0.4369225 0.5596128 0.4436615 0.5532439 0.4496806 0.5475555 0.4550566 0.5424748 0.4598583 0.5379369 0.4641469 0.5338838 0.4679774 0.5302637 0.4713986 0.5270304
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
3.9999199 4.0002079 4.000142 4.0000149 3.999964 3.9999751 3.9999972 4.0000062 4.0000044 4.0000005 3.9999989 3.9999992 4 4 4 4 4 4 4 4 4 4 4 4 4
62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
3.9700625 4.0282932 3.9732609 4.0252704 3.9761177 4.0225706 3.9786692 4.0201592 3.9809481 4.0180054 3.9829836 4.0160818 3.9848016 4.0143636 3.9864253 4.012829 3.9878756 4.0114584 3.989171 4.0102342 3.9903279 4.0091408 3.9913613 4.0081642 3.9922842 4.007292 3.9931085 4.0065129 3.9938448 4.0058171 3.9945024 4.0051956 3.9950898 4.0046405 3.9956144 4.0041448 3.9960829 4.0037019 3.9965014 4.0033064 3.9968752 4.0029532 3.997209 4.0026377 3.9975072 4.0023559 3.9977735
-1.006758 -0.993614 -1.006036 -0.994296 -1.005391 -0.994905 -1.004815 -0.99545 -1.0043 -0.995936 -1.003841 -0.99637 -1.003431 -0.996758 -1.003064 -0.997104 -1.002737 -0.997414 -1.002444 -0.99769 -1.002183 -0.997937 -1.00195 -0.998157 -1.001742 -0.998354 -1.001556 -0.99853 -1.001389 -0.998687 -1.001241 -0.998827 -1.001108 -0.998953 -1.00099 -0.999064 -1.000884 -0.999164 -1.00079 -0.999254 -1.000705 -0.999333 -1.00063 -0.999405 -1.000563 -0.999468 -1.000503
0.4744543 0.5241426 0.4771835 0.5215632 0.4796212 0.5192595 0.4817984 0.5172018 0.483743 0.515364 0.4854799 0.5137226 0.4870312 0.5122565 0.4884167 0.510947 0.4896543 0.5097775 0.4907596 0.5087329 0.4917468 0.5077999 0.4926286 0.5069666 0.4934161 0.5062223 0.4941195 0.5055575 0.4947478 0.5049637 0.4953089 0.5044334 0.4958101 0.5039598 0.4962577 0.5035367 0.4966575 0.5031589 0.4970146 0.5028214 0.4973336 0.5025199 0.4976185 0.5022507 0.4978729 0.5020103 0.4981002
109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155
4.0021042 3.9980114 4.0018794 3.9982239 4.0016786 3.9984136 4.0014992 3.9985831 4.0013391 3.9987345 4.001196 3.9988697 4.0010682 3.9989904 4.0009541 3.9990983 4.0008522 3.9991946 4.0007611 3.9992807 4.0006798 3.9993575 4.0006072 3.9994262 4.0005423 3.9994875 4.0004844 3.9995422 4.0004326 3.9995911 4.0003864 3.9996348 4.0003451 3.9996738 4.0003082 3.9997087 4.0002753 3.9997398 4.0002459 3.9997676 4.0002196 3.9997924 4.0001962 3.9998146 4.0001752 3.9998344 4.0001565
-0.999525 -1.000449 -0.999576 -1.000401 -0.999621 -1.000358 -0.999662 -1.00032 -0.999698 -1.000286 -0.99973 -1.000255 -0.999759 -1.000228 -0.999785 -1.000204 -0.999808 -1.000182 -0.999828 -1.000162 -0.999847 -1.000145 -0.999863 -1.00013 -0.999878 -1.000116 -0.999891 -1.000103 -0.999902 -1.000092 -0.999913 -1.000082 -0.999922 -1.000074 -0.99993 -1.000066 -0.999938 -1.000059 -0.999944 -1.000052 -0.99995 -1.000047 -0.999956 -1.000042 -0.99996 -1.000037 -0.999965
0.5017955 0.4983031 0.5016037 0.4984844 0.5014323 0.4986463 0.5012793 0.498791 0.5011426 0.4989201 0.5010206 0.4990355 0.5009115 0.4991385 0.5008141 0.4992306 0.5007272 0.4993128 0.5006495 0.4993862 0.5005801 0.4994518 0.5005181 0.4995104 0.5004628 0.4995627 0.5004133 0.4996094 0.5003692 0.4996511 0.5003297 0.4996884 0.5002945 0.4997217 0.500263 0.4997514 0.5002349 0.499778 0.5002098 0.4998017 0.5001874 0.4998229 0.5001674 0.4998418 0.5001495 0.4998587 0.5001335
156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202
3.9998521 4.0001398 3.9998679 4.0001248 3.999882 4.0001115 3.9998946 4.0000996 3.9999059 4.0000889 3.9999159 4.0000794 3.9999249 4.000071 3.9999329 4.0000634 3.9999401 4.0000566 3.9999465 4.0000506 3.9999522 4.0000452 3.9999573 4.0000403 3.9999619 4.000036 3.999966 4.0000322 3.9999696 4.0000287 3.9999728 4.0000257 3.9999757 4.0000229 3.9999783 4.0000205 3.9999806 4.0000183 3.9999827 4.0000163 3.9999846 4.0000146 3.9999862 4.000013 3.9999877 4.0000116 3.999989
-1.000033 -0.999968 -1.00003 -0.999972 -1.000027 -0.999975 -1.000024 -0.999978 -1.000021 -0.99998 -1.000019 -0.999982 -1.000017 -0.999984 -1.000015 -0.999986 -1.000014 -0.999987 -1.000012 -0.999989 -1.000011 -0.99999 -1.00001 -0.999991 -1.000009 -0.999992 -1.000008 -0.999993 -1.000007 -0.999994 -1.000006 -0.999994 -1.000005 -0.999995 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.4998738 0.5001193 0.4998873 0.5001065 0.4998993 0.5000951 0.4999101 0.500085 0.4999197 0.5000759 0.4999283 0.5000678 0.4999359 0.5000605 0.4999428 0.5000541 0.4999489 0.5000483 0.4999544 0.5000431 0.4999592 0.5000385 0.4999636 0.5000344 0.4999675 0.5000307 0.499971 0.5000275 0.4999741 0.5000245 0.4999768 0.5000219 0.4999793 0.5000196 0.4999815 0.5000175 0.4999835 0.5000156 0.4999853 0.5000139 0.4999868 0.5000124 0.4999882 0.5000111 0.4999895 0.5000099 0.4999906
203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249
4.0000104 3.9999902 4.0000093 3.9999912 4.0000083 3.9999922 4.0000074 3.999993 4.0000066 3.9999937 4.0000059 3.9999944 4.0000053 3.999995 4.0000047 3.9999955 4.0000042 3.999996 4.0000038 3.9999964 4.0000034 3.9999968 4.000003 3.9999972 4.0000027 3.9999975 4.0000024 3.9999977 4.0000021 3.999998 4.0000019 3.9999982 4.0000017 3.9999984 4.0000015 3.9999986 4.0000014 3.9999987 4.0000012 3.9999989 4.0000011 3.999999 4.000001 3.9999991 4.0000009 3.9999992 4.0000008
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.5000089 0.4999916 0.5000079 0.4999925 0.5000071 0.4999933 0.5000063 0.499994 0.5000056 0.4999947 0.500005 0.4999952 0.5000045 0.4999957 0.500004 0.4999962 0.5000036 0.4999966 0.5000032 0.499997 0.5000029 0.4999973 0.5000026 0.4999976 0.5000023 0.4999978 0.500002 0.4999981 0.5000018 0.4999983 0.5000016 0.4999985 0.5000015 0.4999986 0.5000013 0.4999988 0.5000012 0.4999989 0.500001 0.499999 0.5000009 0.4999991 0.5000008 0.4999992 0.5000007 0.4999993 0.5000007
250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283
3.9999993 4.0000007 3.9999993 4.0000006 3.9999994 4.0000006 3.9999995 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.4999994 0.5000006 0.4999994 0.5000005 0.4999995 0.5000005 0.4999996 0.5000004 0.4999996 0.5000004 0.4999996 0.5000003 0.4999997 0.5000003 0.4999997 0.5000003 0.4999997 0.5000002 0.4999998 0.5000002 0.4999998 0.5000002 0.4999998 0.5000002 0.4999998 0.5000002 0.4999999 0.5000001 0.4999999 0.5000001 0.4999999 0.5000001 0.4999999 0.5000001
L11 L21 L31
CROUT 0 L22 L32
3 0 6
[L] 0 8 -8
L22 L32
8 -8
0 0 L33
0 0 6
1 0 0
1 0 0
L33
U12 1 0
U13 U23 1
[U] 1.6666667 0.6666667 1 0.25 0 1
6
3 0 6
[L] 0 8 -8
y11 y21 y31
2.6666667 -0.875 0.5
1 0 0
x11 x21 x31
gauss seidel 5 8 2
2 2 8
x2 0 -0.875 -1.242188 -1.175293 -1.022919 -0.958113 -0.969276 -0.995808 -1.007243 -1.005384 -1.000765 -0.998748 -0.999057 -0.999861 -1.000216
x3 0 1.46875 1.2011719 0.5916748 0.3324509 0.3771052 0.4832308 0.5289719 0.5215371 0.5030609 0.4949914 0.4962261 0.4994424 0.5008657 0.5006612
8 -7 26
0 0 6
[U] 1.6666667 0.6666667 1 0.25 0 1
4 -1 0.5
-1.000165 -1.000025 -0.999963 -0.999971 -1 -1.000006 -1.000005 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0.5001014 0.4998504 0.4998842 0.4999816 0.5000258 0.5000203 0.5000033 0.4999955 0.4999964 0.4999994 0.5000008 0.5000006 0.5000001 0.4999999 0.4999999 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
[Y] 2.6666667 -0.875 0.5
[X] 4 -1 0.5
=
=
[B] 8 -7 26
[Y] 2.6666667 -0.875 0.5
GAUSS JACOBI 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 1 0 0 0 -1
0 0 0 1000 0 0
1 0 0 0 0 0 va
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 1 0 0
0 0 0.6 1 1.6 -0.8
0 0 iterasi 0 1 0 iterasi 1 0 0 iterasi 2 0 -1666.66666667 iterasi 3 0 -1333.33333333 iterasi 4 -1 0 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
0 -1 0 0 0 0
ha 0 0 0 0 1000 -666.667 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0 500 0
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56 iterasi 57 iterasi 58 iterasi 59 iterasi 60 iterasi 61 iterasi 62 iterasi 63 iterasi 64 iterasi 65 iterasi 66 iterasi 67 iterasi 68 iterasi 69 iterasi 70 iterasi 71 iterasi 72 iterasi 73 iterasi 74 iterasi 75 iterasi 76 iterasi 77 iterasi 78 iterasi 79 iterasi 80 iterasi 81 iterasi 82
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iterasi 83 iterasi 84 iterasi 85 iterasi 86 iterasi 87 iterasi 88 iterasi 89 iterasi 90 iterasi 91 iterasi 92 iterasi 93 iterasi 94 iterasi 95 iterasi 96 iterasi 97 iterasi 98 iterasi 99 iterasi 100
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 1 0 0
vb
s1 0 0 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 -1666.67 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
0 0 0.6 1 1 0 s2 0 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
0 1 0 0 0 -1
0 0 0 -1666.67 -833.333 -666.667
1 0 0 0 0 0
s3 0 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
iterasi 0 iterasi 1 iterasi 2 iterasi 3 iterasi 4 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
0 0 1000 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
-833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333 -833.333
666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
gauss seidel 0 -1 0 0 0 0
0 0 1 0 0 0
0
0
0 -666.6666667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.6 0.8 0 1 0 0
0 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0 0 0.6 1 1 0
0 0 -1666.67 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333
0 1 0 0 0 -1
0 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
0 0 0 -1666.67 -833.333 -666.667
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
-833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333 -833.333 -833.3333333
666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667 666.6667
va 1 0 0 0 0 0
ha 0 0 0 1 0 0
vb 0 0 -1 0 0 0
s1 -0.6 -0.8 0 0 0.6 0.8
s2 0 0 0.6 -0.8 0.8 -0.6
s3 0 1 -1 0 0 0
=
1 = masukin angka minus 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
0 0 0 1000
0
0
0
-0.8
0.8
0
0
0
0
0
0
-0.8
-1
0
GAUSS JORDAN iterasi 1
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 1 0 0 0 -1
0 0 0 1000 0 0
iterasi 2
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0.6 -0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 -1 0 0 0 -1
0 0 0 1000 0 0
iterasi 3
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0.6 -0.8 0 -0.6 -0.8 0
0 0 0.6 -0.6 0.8 -0.8
0 -1 0 0 0 -1
0 0 0 1000 0 0
iterasi 4
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
-0.6 0.8 0.6 1 1.6 -0.8
0 -1 0 0 0 -1
1000 -1333.333 0 -1666.667 -1333.333 0
iterasi 5
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 -1 0 0 0 -1
500 -666.6667 500 -833.3333 -833.3333 -666.6667
iterasi 6
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
500 0 500 -833.3333 -833.3333 666.66667
c 0 0 0 0 20 0
CROUT [A] 1 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
1 0 0 0
0 -1 0 0
0
0
0
-0.8
0.8
0
0
0
0
0
0
0
-0.8
-1
0
0
L11 L21 L31 L41 L51 L61
1 0 0 0 0 0
L22 L32 L42 L52 L62
-1 0 0 0 0
L33 L43 L53 L63
u12 u13 u14 u15 u16
0 0 0.6 0 0
u23 u24 u25 u26
0 -0.8 0 -1
u34 u35 u36
[L] 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 -0.6 -0.8 0
0 0 0 0 1.6 -0.8
0 0 0 0 0 -1
0.6 -0.8 0 1 0 0
0 0 0.6 1 1 0
0 -1 0 0 0 1
[U] 1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
[L]^-1 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 -1.666667 -0.833333 0.6666667
0 0 0 0 0.625 -0.5
0 0 0 0 0 -1
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
-0.6 0.8 0 1 0 0
0.6 -0.8 -0.6 -1 1 0
0 1 0 0 0 1
[L]
[U]
0 0 1 0
0 0 0 -0.6
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0.6 -0.8 0 1
0 0 0.6 1
0 -1 0 0
0
-0.8
1.6
0
0
0
0
0
1
0
0
0
-0.8
-1
0
0
0
0
0
1
1 0 0 0
L44 L54 L64
-0.6 -0.8 0
L55 L65
1.6 -0.8
L66
-1
0 0.6 0
u45 u46
1 0
u56
0
[Y] 0 0 0 -1666.667 0 0
[B] 0 0 0 1000 0 0
y11 y21 y31 y41 y51 y61
0 0 0 -1666.667 0 0
[Y] 0 0 0 -1666.667 0 0
x11 x21 x31 x41 x51 x61
va ha hc s1 s2 s3
[X] 1000 0 0 -1666.667 0 0
=
1000 0 0 -1666.667 0 0
L 0 0 0 1000 0 0
0 0 0 -1666.667 -833.3333 666.66667
#N/A #N/A #N/A #N/A #N/A #N/A
0 0 0 -1666.667 -833.3333 666.66667
500 1.137E-13 500 -833.3333 -833.3333 666.66667
U
X
Y
DOOLITTLE A
L
1 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0
0
0
-0.8
0.8
0
0
0
0
0
0
0
0
-0.8
-1
0
0
0
U11
1
U12 U22
0 -1
U13 U23 U33
0 0 1
U14 U24 U34 U44
0.6 0.8 0 -0.6
L21 L31 L41 L51 L61
0 0 0 0 0
L32 L42 L52 L62
0 0 0 0
L43 L53 L63
0 0 0
L54 L64
1.3333333 0
=
0 0 0 0 0 1
[Y] y11 y21 y31 y41 y51 y61
=
0 1 0 0 0 -1
[X] x11 x21 x31 x41 x51 x61
[L] 1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 1.3333333 0
0 0 0 0 1 -0.5
[U] 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0.6 0.8 0 -0.6 0 0
0 0 0.6 -0.6 1.6 0
DOOLITTLE L
U 0 0 0 1
0 0 0 0
0 0 0 0
1 0 0 0
0 -1 0 0
0 0 1 0
0.6 0.8 0 -0.6
0 0 0.6 -0.6
0 1 0 0
1.3333333
1
0
0
0
0
0
1.6
0
0
-0.5
1
0
0
0
0
0
-1
U15 U25 U35 U45 U55
0 0 0.6 -0.6 1.6
U16 U26 U36 U46 U56 U66
0 1 0 0 0 -1
[Y] [Y]
= =
[B] [L]^-1
[B]
[L]
L65
[B] 0 0 0 1000 0 0 [Y] 0 0 0 1000 -1333.333 -666.6667
-0.5
[L]^-1 1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 -1.333333 -0.666667
0 0 0 0 1 0.5
=
0 0 0 0 0 1
[B] 0 0 0 1000 0 0
=
0 -1 0 0 0 -1
[Y] 0 0 0 1000 -1333.333 -666.6667
[U]^-1 1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
1 -1.333333 0 -1.666667 0 0
0.375 -0.5 -0.375 -0.625 0.625 0
[Y] 0 0 0 1000 -1333.333 -666.6667 [X] 500 2.274E-13 500 -833.3333 -833.3333 666.66667
GAUSS JACOBI
soal tugas 1 0 0 0 0 0
0 1 0 0 0 0
va iterasi 0 iterasi 1 iterasi 2 iterasi 3 iterasi 4 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.8 -0.6 0.8 0.6 0 0
0 0 -0.6 0.8 0.6 -0.8
1 0 0 0 -1 0
0 0 0 0 0 1
ha
vb
s1
s2
s3
0 0 0 5625 5625 2460.938 2460.938 4240.723 4240.723 3239.594 3239.594 3802.729 3802.729 3485.965 3485.965 3664.145 3664.145 3563.919 3563.919 3620.296 3620.296 3588.584 3588.584 3606.422 3606.422 3596.388 3596.388 3602.032 3602.032 3598.857 3598.857 3600.643 3600.643 3599.638 3599.638 3600.203
0 0 9375 9375 4101.563 4101.563 7067.871 7067.871 5399.323 5399.323 6337.881 6337.881 5809.942 5809.942 6106.908 6106.908 5939.864 5939.864 6033.826 6033.826 5980.973 5980.973 6010.703 6010.703 5993.98 5993.98 6003.386 6003.386 5998.095 5998.095 6001.071 6001.071 5999.397 5999.397 6000.339 6000.339
0 12500 12500 5468.75 5468.75 9423.828 9423.828 7199.097 7199.097 8450.508 8450.508 7746.589 7746.589 8142.544 8142.544 7919.819 7919.819 8045.102 8045.102 7974.63 7974.63 8014.27 8014.27 7991.973 7991.973 8004.515 8004.515 7997.46 7997.46 8001.429 8001.429 7999.196 7999.196 8000.452 8000.452 7999.746
0 0 7500 7500 3281.25 3281.25 5654.297 5654.297 4319.458 4319.458 5070.305 5070.305 4647.954 4647.954 4885.526 4885.526 4751.892 4751.892 4827.061 4827.061 4784.778 4784.778 4808.562 4808.562 4795.184 4795.184 4802.709 4802.709 4798.476 4798.476 4800.857 4800.857 4799.518 4799.518 4800.271 4800.271
0 0 10000 10000 4375 4375 7539.063 7539.063 5759.277 5759.277 6760.406 6760.406 6197.271 6197.271 6514.035 6514.035 6335.855 6335.855 6436.081 6436.081 6379.704 6379.704 6411.416 6411.416 6393.578 6393.578 6403.612 6403.612 6397.968 6397.968 6401.143 6401.143 6399.357 6399.357 6400.362 6400.362
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56 iterasi 57 iterasi 58 iterasi 59 iterasi 60 iterasi 61 iterasi 62 iterasi 63 iterasi 64 iterasi 65 iterasi 66 iterasi 67 iterasi 68 iterasi 69 iterasi 70 iterasi 71 iterasi 72 iterasi 73 iterasi 74 iterasi 75 iterasi 76 iterasi 77 iterasi 78 iterasi 79 iterasi 80 iterasi 81 iterasi 82
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3600.203 3599.886 3599.886 3600.064 3600.064 3599.964 3599.964 3600.02 3600.02 3599.989 3599.989 3600.006 3600.006 3599.996 3599.996 3600.002 3600.002 3599.999 3599.999 3600.001 3600.001 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600
5999.809 5999.809 6000.107 6000.107 5999.94 5999.94 6000.034 6000.034 5999.981 5999.981 6000.011 6000.011 5999.994 5999.994 6000.003 6000.003 5999.998 5999.998 6000.001 6000.001 5999.999 5999.999 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000
7999.746 8000.143 8000.143 7999.92 7999.92 8000.045 8000.045 7999.975 7999.975 8000.014 8000.014 7999.992 7999.992 8000.005 8000.005 7999.997 7999.997 8000.001 8000.001 7999.999 7999.999 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000
4799.847 4799.847 4800.086 4800.086 4799.952 4799.952 4800.027 4800.027 4799.985 4799.985 4800.009 4800.009 4799.995 4799.995 4800.003 4800.003 4799.998 4799.998 4800.001 4800.001 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800
6399.797 6399.797 6400.114 6400.114 6399.936 6399.936 6400.036 6400.036 6399.98 6399.98 6400.011 6400.011 6399.994 6399.994 6400.004 6400.004 6399.998 6399.998 6400.001 6400.001 6399.999 6399.999 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400
iterasi 83 iterasi 84 iterasi 85 iterasi 86 iterasi 87 iterasi 88 iterasi 89 iterasi 90 iterasi 91 iterasi 92 iterasi 93 iterasi 94 iterasi 95 iterasi 96 iterasi 97 iterasi 98 iterasi 99 iterasi 100
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600
6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000
8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000
4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800
6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400
CONTOH SOAL TUGAS TERDAHULU 0 0 0 10000 0 0
iterasi 0 iterasi 1 iterasi 2 iterasi 3 iterasi 4 iterasi 5 iterasi 6 iterasi 7 iterasi 8 iterasi 9 iterasi 10 iterasi 11 iterasi 12 iterasi 13 iterasi 14 iterasi 15 iterasi 16 iterasi 17 iterasi 18 iterasi 19 iterasi 20 iterasi 21 iterasi 22 iterasi 23 iterasi 24 iterasi 25 iterasi 26 iterasi 27 iterasi 28 iterasi 29 iterasi 30 iterasi 31 iterasi 32 iterasi 33 iterasi 34 iterasi 35
1 0 0 0 0 0
0 1 0 0 0 0
-0.8 -0.6 0.8 0.6 0 0
0 0 -0.6 0.8 0.6 -0.8
1 0 0 0 -1 0
0
0
0
0
0 -7500 4218.75 -2373.05 1334.839 -750.847 422.3514 -237.573 133.6346 -75.1695 42.28283 -23.7841 13.37855 -7.52543 4.233057 -2.38109 1.339366 -0.75339 0.423784 -0.23838 0.134088 -0.07542 0.042426 -0.02386 0.013424 -0.00755 0.004247 -0.00239 0.001344 -0.00076 0.000425 -0.00024 0.000135 -7.57E-05 4.26E-05
0 0 5625 2460.9375 4240.722656 3239.593506 3802.728653 3485.965133 3664.144613 3563.918655 3620.295756 3588.583637 3606.421704 3596.387791 3602.031867 3598.857075 3600.642896 3599.638371 3600.203416 3599.885578 3600.064362 3599.963796 3600.020365 3599.988545 3600.006443 3599.996376 3600.002039 3599.998853 3600.000645 3599.999637 3600.000204 3599.999885 3600.000065 3599.999964 3600.00002
0 9375 4101.563 7067.871 5399.323 6337.881 5809.942 6106.908 5939.864 6033.826 5980.973 6010.703 5993.98 6003.386 5998.095 6001.071 5999.397 6000.339 5999.809 6000.107 5999.94 6000.034 5999.981 6000.011 5999.994 6000.003 5999.998 6000.001 5999.999 6000 6000 6000 6000 6000 6000
0 12500 5468.75 9423.828 7199.097 8450.508 7746.589 8142.544 7919.819 8045.102 7974.63 8014.27 7991.973 8004.515 7997.46 8001.429 7999.196 8000.452 7999.746 8000.143 7999.92 8000.045 7999.975 8000.014 7999.992 8000.005 7999.997 8000.001 7999.999 8000 8000 8000 8000 8000 8000 8000
7500 3281.25 5654.296875 4319.458008 5070.304871 4647.95351 4885.52615 4751.89154 4827.061009 4784.778183 4808.562272 4795.183722 4802.709156 4798.476099 4800.857194 4799.517828 4800.271222 4799.847438 4800.085816 4799.951728 4800.027153 4799.984727 4800.008591 4799.995167 4800.002718 4799.998471 4800.00086 4799.999516 4800.000272 4799.999847 4800.000086 4799.999952 4800.000027 4799.999985 4800.000009
iterasi 36 iterasi 37 iterasi 38 iterasi 39 iterasi 40 iterasi 41 iterasi 42 iterasi 43 iterasi 44 iterasi 45 iterasi 46 iterasi 47 iterasi 48 iterasi 49 iterasi 50 iterasi 51 iterasi 52 iterasi 53 iterasi 54 iterasi 55 iterasi 56
-2.39E-05 1.35E-05 -7.58E-06 4.26E-06 -2.4E-06 1.35E-06 -7.59E-07 4.27E-07 -2.4E-07 1.35E-07 -7.59E-08 4.27E-08 -2.4E-08 1.35E-08 -7.6E-09 4.28E-09 -2.41E-09 1.35E-09 -7.62E-10 4.29E-10 -2.42E-10
3599.999989 3600.000006 3599.999996 3600.000002 3599.999999 3600.000001 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600 3600
6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000
8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000
4799.999995 4800.000003 4799.999998 4800.000001 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800 4800
0 0 0 0 0 1
0 10000 4375 7539.063 5759.277 6760.406 6197.271 6514.035 6335.855 6436.081 6379.704 6411.416 6393.578 6403.612 6397.968 6401.143 6399.357 6400.362 6399.797 6400.114 6399.936 6400.036 6399.98 6400.011 6399.994 6400.004 6399.998 6400.001 6399.999 6400 6400 6400 6400 6400 6400 6400
0 0 0 10000 0 0
6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400 6400
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