On Sun, Oct 30, 2011 at 10:52 AM, Matthew Knepley <knepley at gmail.com> wrote:
> More commentary: There are lots of papers about estimating these norms > (1-norms too), and > nothing works well. There are no good ways to generically approximate the > matrix norm. For > certain very special classes of matrix, you can do it, but these are also > the matrices for which > you have a specialize very fast solver, like the Laplacian, so you rarely > care. > > There is a nice paper by John D. Dixon, "Estimating Extremal Eigenvalues and Condition Numbers of Matrices", http://www.jstor.org/pss/2157241, which provides an extremely robust method for getting rough estimates of the condition number, and it only requires the ability to apply your operator and its adjoint. A typical usage would be to compute an estimate of the condition number K, such that the true condition number is within a factor of 2 of K with a probability of 1-10^-6. The 1-norm is actually pretty trivial to compute if you have access to your matrix entries; it is the maximum vector one norm of the columns of the matrix. Jack -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20111030/eee27282/attachment.htm>
