Let A = 3.1415 1.4142 2.7183 1.4142 0.2505 0.5143 2.7183 0.5143 0.1116 (i) Calculate cond (A) = ||A||||A¹|| (ii) Let A' = [ 3.142 1.414 2.718 1.414 0.251 0.514 2.718 0.514 0.112 Let x and x' be the solution to Ax = b and A'x = b, respectively, Ix-x for some b € R³. Find a bound for the relative error -).(< Ixx
Let A = 3.1415 1.4142 2.7183 1.4142 0.2505 0.5143 2.7183 0.5143 0.1116 (i) Calculate cond (A) = ||A||||A¹|| (ii) Let A' = [ 3.142 1.414 2.718 1.414 0.251 0.514 2.718 0.514 0.112 Let x and x' be the solution to Ax = b and A'x = b, respectively, Ix-x for some b € R³. Find a bound for the relative error -).(< Ixx
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
hello can u do this question for me
![(a) Let
A =
Given
Question 1
3.1415 1.4142 2.7183
1.4142 0.2505 0.5143
2.7183 0.5143 0.1116
(i) Calculate cond (A) = || A||||A¹||∞.
(ii) Let
A' =
3.142 1.414 2.718
1.414 0.251 0.514
2.718 0.514 0.112
Let x and x' be the solution to Ax = b and A'x = b, respectively,
for some b
R³. Find a bound for the relative error (x-x').
²).(²
1x
4-[44] and b-[4]
A =
1. (i) Compute the singular value decomposition of A and use it to deter-
mine A+. (A+ is the Moore-Penrose pseudoinverse).
(
(ii) Use A+ to find a least squares solution to the Ax = b.
(iii) Show that A+ AA+ = A+.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c044b69-454e-4f9e-8cd6-567ae6231ec2%2F74a3701d-a146-4c8b-9c11-157ba6f0dd15%2F2jt5pps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Let
A =
Given
Question 1
3.1415 1.4142 2.7183
1.4142 0.2505 0.5143
2.7183 0.5143 0.1116
(i) Calculate cond (A) = || A||||A¹||∞.
(ii) Let
A' =
3.142 1.414 2.718
1.414 0.251 0.514
2.718 0.514 0.112
Let x and x' be the solution to Ax = b and A'x = b, respectively,
for some b
R³. Find a bound for the relative error (x-x').
²).(²
1x
4-[44] and b-[4]
A =
1. (i) Compute the singular value decomposition of A and use it to deter-
mine A+. (A+ is the Moore-Penrose pseudoinverse).
(
(ii) Use A+ to find a least squares solution to the Ax = b.
(iii) Show that A+ AA+ = A+.
Expert Solution
Step 1
Given : matrix
(i) Calculate
(ii) Let
and and be the solution to and respectively for some .
We have to find a bound for the relative error
Step by step
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