Suggestions For Problem Set 3.docx

Suggestions for Problem Set 3 1. Can we cite the theorem wherein the positive definite matrices will have the said condition numbers? For a positive definite matrix (all eigenvalues positive) the solution vector and error term always satisfy:

||x|| ≥ ||b||/max and ||x|| ≤ ||b||/min

Therefore the relative error is bounded by ||x||/||x|| ≤ ||b||/||b|| (max/min) The ratio (max/min) is known as the condition number of A. 2. Regarding the code, I think we should print the value of the solution vector apart from the residual and error norms because it was stated in the problem that we should approximate the solution so I guess we should print it out.  3. Kindly check the documentation… 4. If ever, kindly send the tabulations for the results so that I can assist/help/contribute in making the assessment of the results.  “Di ko po kc ma-run dito ng maayos…” 5. Attach is my coding for the LU kindly check where I went wrong.. di ko na kasi Makita tapos nahirapan ako kung backward ba o forward mauna… Thank you so much