Numerical Lecture 4

l-e/*\+r,L l Rea[ R^eotb o+ po{,6rwn^e'\elwLnlni j -^" u\dlr-c the, pot6not-n.de{{qrLon

i O P ^l t ) = c i

t^,lr,ere

aoin+ o,f1 *.fi l@'p-,L'.)"

--u r or,^.

I

I

bb

i

u

'

; r / g w t o n - k'tp h " o r . rtec \-'\s'n - h e ^ eg ;"',t.

I O a-rr z tn - 9d\) i

pl

C" rre c*ioh te--,rwr

i

V6 w\en U"ict y P-(r l bJ trc-rc. ; o ? J7ree (gnE$q"t

ta^)

tv<- olat r,i vr. ^ qrtaglte,lh

ct"d eL

.(^.

Y-e'nori-.d er

*r

(re-tn er,i.n"de'rtheore.-

ctP (12r^et )

€tnr'','e*t-u,p @ c1- -- ?L6

u, e- h91uq

wz dettaTc b& Q*,nLr)

vn-l , uhiJ

P,* t*) -- (_q--1L^)Q_n.(*)

i^

qbov."

, tKet v,...t p^(r.',,) l5

P , l yr . tr-_ * ^_ ,r, )

1-

0..

Fo l o rr -bcx'{ *^A

v^r'e- l"'otye

P* ttr ,',) = f

Cl,r."J

-t- (z*-e-" ) G.-^-,(r) t*).Q^.-,L.) Pl,

q,. J-

P,,..t.t^)= Q^_,L1") al'^"i'k..tbo

3,^-"L*)

4n J

Por Q--,-,L*)

wel'ts.ve

= (q--sLn) S,*-rL*) f S

CL^_,(l)

t

@

ie

ghe-

%nohenYol-de6re'em-2-

e-rnuinder u.lhen Qn.(*-l P'^ t7.^ ) =- S'

qnd,

is d-i,riJ*d bJ t"t--l.")

D ,, + @ be-u^ph' f lve e-c( t'Lqho

t*,:-{,"- ? T\,tr

lt't'ons bs t'!'g- fuotE t:-P-.P''t".1to g6iv c u,cc-e eb PPgrt-u"

a

lui:i,rns.

C-a,nb e- fu u." d. bg ccrrr6 ig Ocet b,.,o ^/0d Qo{

Putde-te<-vrui*;brr5 '-t

tYl.

m - 1'r

q.r{'

vn-j

)'ln

+ b,ec."r'r- + f"2?,^d';-*-*b*h

cr.bsve

?rot,

bo = €t, b t -- ct t tq(",bo bz- : Ctz-1g-*bt

flo = b"

Qr= br -bot^ 4L -b.-b,

>

*'

1*"b.]

* )+\c'n-,

u"Ji'*

q-2

rr.r-3

vA-2-

r b, a t bzt

a,rl'' ; "^^r ot,-= lt--\)tbr't'

Yn-l

e.

n-l

w-2

( bo"J -b,.J-l u" J-i -( -bo"L^t

we- Cq'" c-l ri\

b-b = *?*q-"bL

cl'--ba-b'e('n

t I

t

t

Ortr = f -{.bYn-\

f t

te

Qt$cnrrzrt

ie

=b'^

I-= Qr",tt^b.{

wrpuQe thr-

\g.at

"4vqtflon

ftV

pctttern b5 re-\qbeJ'lt'i'"4t\'e rc-nn.ti,'Ler r n t binto {C"it 'then the_ b'5 C-r,,'.,\ae tLe t^e-ertrrg c€S-off{ne;\as4 re-Qton

be:cto

iJlt

,bn--e{.€tt,,bn.

$e-"too^? the Coe-(/-l.cie^t, o+

b

n-z

L*l

co t((t*rc"^_

wg, Mv<,

onJ

tbo #-!

b,f

-'-t

1wt

,,wL m-5

b z/-3*

*+b *.)

+'' 4'-") e'1L

=Lt-%) ic"i;

+5

o C*_ra^ ) tS b" =Co b,: cr -Cot^ r

Cu--bo c, ;l b r t C , r e t - , ,

>

r

i

5-- b--r*tr',C^-t=Qrn-t

b^_,:t-%^C--r

\

to; New to n -Rqphaon ur.,eluly g. L^* r = a-n -- b-

Crr, _t

r h i:

rn-oU 8+co-rton t s Fr.o *.^

A$tf{tt*

I}irye -$rett

o+

crs

n

crl

b\r3e- Vte,tq

c-cr.n be- e-ocp\o.i*b5

to0furi$ r^etl'..r J. t @{ eqn Co\otrr{q-t fui/rri% q.

bo

a\

ctz

tnb o

t"br

q*1

qL^bz_

es ! r

bt"q

bt \co

Co

c(j

Cr

CL

Ez-q-ple: uoc the

9L^b* -l

b*

r)a.-cdr.\ tOrn-r

L^crn !!s\

Cb

-.-

c*_,

gir3e-vr'etq rne-thodt,, {."1 the-rGor

8 r - 3 - x o t - - y 6 : c + 3 3= o B. oouco

t"tble.

-le.cocc:c 6 6 ' a oc o c

S . a o o o r r - t 3 .6 o s o c

6'qaaoa ? :, C o a a a ')Lrz 9co:0.?t%\22

-7')0ooo \--

+

cbr bo 0 " 8 -26.ccccc - \ 0 '$0o'''o -16'Zzooc

3A'occec -1,).bo{oc 3 . q , 1 6 0o

- b "-l6noo - 4z' |ttgoo

-3-A?ba'e = 0'8ooo,l

L-q"r- 6 ttso")

A-r- O' Ziolg? Z"rso00o

-LCI.0e0oa

-r-6'grrottc

1,rCbflL

S,ccceo

8 osao0

-t2,gnrcfu

33'1oCIoe

-tt'(.:'6b5 -33'go\o

-3?.q"|65) -0,9olcL

7.o51)2.

-5 i?33o

-b.6agtg

-qL'6fi8'r

(-o yoloL) %z --q*, +r=- Q'8I\9' ffi2;9 \--

= () 9xl 22 the foq,rJ.J to"

flo*"

de'n'"^^fp\otee ( s

' d= C 8 ? I O f'*^d q,,d ot).et Yoots Cqnbe

' \ \ a 1w t t * A

gq]-L|1L,-L6x-f331t91-o.8BI0)tgr.-rz-2t.t(t_ 3'T.\166 )

oA

then g ' f - t ? - ' ) q (l t ' - ' ) - + ' \ t 6 6 = o

A^d

lL e ofl-.e r

roo t5

- \ - 7 ' g w) b \ t 8 o

ct Y ?'