
Re: Condition number of matrices
Posted:
Jul 5, 2006 3:36 PM


Toni Lassila <toni@nukespam.org> wrote:
> If you can do SVD,
Doing an SVD as an aid in solving a linear system is not very practical.
Lapack (maybe inherited from Linpack?) has a condition estimator which implicitly assumes that solving A^{1}x is cheap. This is true for dense systems, if the matrix has already been factored. The factorization has N^3 cost, the solution N^2, so wasting a couple of solutions is acceptable.
You can probably do the same thing for sparse matrices, if you use a direct solver.
The remaining, though unfortunately rather important case, is sparse systems and iterative methods. There, you construct your Hessenberg matrix during the iteration process, and estimate its singular or eigen values.
Victor.  Victor Eijkhout  eijkhout at tacc utexas edu ph: 512 471 5809

