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

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Fijoy George

Posts: 97
Registered: 12/13/04
Condition number of matrices
Posted: Jul 2, 2006 5:45 PM
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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)?

Thank you very much
Fijoy





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