OK. Thanks again. On Sun, Oct 30, 2011 at 8:10 PM, Jack Poulson <jack.poulson at gmail.com>wrote:
> Not a problem; though for some reason I repeatedly wrote "condition > number" when I meant "two norm". Dixon's paper certainly provides a method > for computing an estimate to the condition number, but the latter also > requires the ability to apply the inverse of your operator and the inverse > of its adjoint. > > Jack > > > On Sun, Oct 30, 2011 at 11:33 AM, behzad baghapour < > behzad.baghapour at gmail.com> wrote: > >> 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 >> ================================== >> >> > -- ================================== 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/20111030/6d0bcfe5/attachment-0001.htm>
