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Topic: Condition number of matrices
Replies: 5   Last Post: Jul 5, 2006 3:36 PM

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Toni Lassila

Posts: 536
Registered: 12/13/04
Re: Condition number of matrices
Posted: Jul 2, 2006 5:45 PM
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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).



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