Date: Jul 2, 2006 5:45 PM
Author: Toni Lassila
Subject: Re: Condition number of matrices
On Sun, 2 Jul 2006 17:25:32 -0500, "Fijoy George"

<tofijoy@yahoo.co.in> wrote:

>Hi all,

>

>I have the following question regarding the sensitivity analysis of linear

>systems.

>

>In my numerical methods course, I have learned theorems which give upper

>bounds for the relative change in the solution of the linear system Ax=f.

>For example, if only f is changed, relative change in x = K(A)*relative

>change in f, where K(A) is the condition number of the matrix A.

>

>Now, for such theorems to be useful in practice, we need the condition

>number of A which is defined as ||A||*||A_inverse||.

>

>So how does one calculate the condition number of a matrix? Given that real

>world systems are large, can we precisely calculate K(A)? Or, can we only

>hope to obtain a upper bound for K(A)?

If you can do SVD, K(A)_2 = s_max(A) / s_min(A).