maximum condition number in ZGESVD

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maximum condition number in ZGESVD

Postby gcdiwan » Thu Oct 18, 2012 6:23 pm

Hi,

What is the maximum condition number up to which the solution from ZGESVD can be trusted?

G.
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Re: maximum condition number in ZGESVD

Postby Julien Langou » Thu Oct 18, 2012 10:37 pm

The saying is: "The condition number of the condition number is the condition number."

1) Computing the condition number with ZGESVD is expensive but it is very accurate and robust. You can hardly do better. (You can do better with Jacobi SVD.)

2) ZGESVD computes the largest singular value of A (sigma_max) with full accuracy, the smallest one (sigma_min) is only computed up to eps.sigma_max precision.
So sigma_min can have some large error if the condition number is large. This said for most problem, you will have a good idea of what the conditon number is.

Julien.
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