(a) For A A1: i. Solve the system Ax =b and the perturbed system Ax = b; %3D ii. Calculate the relative error ||ox||/ ||x|| and the relative residual ||öb|| / ||b|: iii. Find the condition number of A, and check that ||5x|| < cond(A) || || ||||
(a) For A A1: i. Solve the system Ax =b and the perturbed system Ax = b; %3D ii. Calculate the relative error ||ox||/ ||x|| and the relative residual ||öb|| / ||b|: iii. Find the condition number of A, and check that ||5x|| < cond(A) || || ||||
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![6. Let
A1
10
b =
%3D
40
1 5
A2
9.
4 1]
b =
%3D
41
and use the 1-norm in answering the following questions.
(a) For A A1:
i. Solve the system Ax = b and the perturbed system Aây = b;
%3D
ii. Calculate the relative error ||ox||/ ||x|| and the relative residual ||ob|| / ||b|:
iii. Find the condition number of A, and check that
S cond(A)ob||
||||
||5||
||S||
(c) Which matrix A = A1 or A2 is more susceptible to error when solving Ax = b, if
the entries of b are subject to rounding or measurement error? Why?
%3D
(b) Repeat part (a) with A = A2.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbff91832-d6e3-4d15-9b02-f5e61d7ebdc6%2F370ec150-41fd-473d-ac53-2e59a3587ae7%2F95gec6n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Let
A1
10
b =
%3D
40
1 5
A2
9.
4 1]
b =
%3D
41
and use the 1-norm in answering the following questions.
(a) For A A1:
i. Solve the system Ax = b and the perturbed system Aây = b;
%3D
ii. Calculate the relative error ||ox||/ ||x|| and the relative residual ||ob|| / ||b|:
iii. Find the condition number of A, and check that
S cond(A)ob||
||||
||5||
||S||
(c) Which matrix A = A1 or A2 is more susceptible to error when solving Ax = b, if
the entries of b are subject to rounding or measurement error? Why?
%3D
(b) Repeat part (a) with A = A2.
%3D
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