Conclude that ||A||F E0, where ơ1 > 02 >... > o,n 2 0 are the singular values of A. Using what we know about the SVD of A-1 given the SVD of A, find Kf(A), the condition number for A in Frobenius norm, in terms of the singular values of A. (It will be a nasty-looking expression. Don't be scared. It cannot be simplified.)
Conclude that ||A||F E0, where ơ1 > 02 >... > o,n 2 0 are the singular values of A. Using what we know about the SVD of A-1 given the SVD of A, find Kf(A), the condition number for A in Frobenius norm, in terms of the singular values of A. (It will be a nasty-looking expression. Don't be scared. It cannot be simplified.)
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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We can use the lemma I showed in the second images directly
Transcribed Image Text:||4||F = ||U A||F for any orthogonal n × n matrix U.
||4||F = ||AVI|f for any orthogonal n x n matrix V.
Transcribed Image Text:a) Conclude that ||A||F =
E0?, where ơ1 > 02 > ... > on 2 0 are the singular
values of A.
b) Using what we know about the SVD of A-' given the SVD of A, find kf(A), the
condition number for A in Frobenius norm, in terms of the singular values of A.
(It will be a nasty-looking expression. Don't be scared. It cannot be simplified.)
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