
Re: Condition number of matrices
Posted:
Jul 2, 2006 5:45 PM


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).

