A good paper, I will work on it. Thanks a lot dear Jack. On Sun, Oct 30, 2011 at 7:54 PM, Jack Poulson <jack.poulson at gmail.com>wrote:
> 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 > -- ================================== Behzad Baghapour Ph.D. Candidate, Mechecanical Engineering University of Tehran, Tehran, Iran https://sites.google.com/site/behzadbaghapour Fax: 0098-21-88020741 ================================== -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20111030/1fbddb35/attachment.htm>
