(i) Let ž. be an approximate solution. Calculate the relative forward error, relative back- ward error, and error magnification factor for this approximate solution (use infinity norm). (ii) Find the condition number of matrix A (using infinity norm). (ii) For a system of linear equations Af = b, what is the possible consequence of an extremely large condition number of A?

(i) Let ž. be an approximate solution. Calculate the relative forward error, relative back- ward error, and error magnification factor for this approximate solution (use infinity norm). (ii) Find the condition number of matrix A (using infinity norm). (ii) For a system of linear equations Af = b, what is the possible consequence of an extremely large condition number of A?

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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Question

5.(10 pts) Given that =
is the exact solution of the linear system of equations Ai = 6
with
-2
1
A =
2
-3
(i) Let ze
be an approximate solution. Calculate the relative forward error, relative back-
ward error, and error magnification factor for this approximate solution (use infinity norm).
(ii) Find the condition number of matrix A (using infinity norm).
(iii) For a system of linear equations A = 6, what is the possible consequence of an extremely large
condition number of A?

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