Let A be a 3 x 3 matrix. Suppose you run the steepest descent algorithm to solve Ax b with b (1, 1, 3)^t. Suppose your stopping condition is || Ax") -b|| < 0.01, |b|| || Ax6)-b|| and suppose your program stops at the 5th iteration where it computes x(5) ,and 0.0056 Suppose cond(A) = 1000. We learned that with a high condition number, ||x5) – x||/||x|| might still be large where x is the true solution to Ax = b. a) What is the largest that ||x(5) - x||/||x|| could theoretically be? (Hint: use the general inequality involving condition number) ||Ax)-b|| b) What should our tolerance (tol) be to guarantee that ||xk) – x||/||x|| < 0.01 ? Our program will still use the stopping condition < tol b| (Hint: use the general inequality involving condition number))

Let A be a 3 x 3 matrix. Suppose you run the steepest descent algorithm to solve Ax b with b (1, 1, 3)^t. Suppose your stopping condition is || Ax") -b|| < 0.01, |b|| || Ax6)-b|| and suppose your program stops at the 5th iteration where it computes x(5) ,and 0.0056 Suppose cond(A) = 1000. We learned that with a high condition number, ||x5) – x||/||x|| might still be large where x is the true solution to Ax = b. a) What is the largest that ||x(5) - x||/||x|| could theoretically be? (Hint: use the general inequality involving condition number) ||Ax)-b|| b) What should our tolerance (tol) be to guarantee that ||xk) – x||/||x|| < 0.01 ? Our program will still use the stopping condition < tol b| (Hint: use the general inequality involving condition number))

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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