[petsc-users] How to calculate Induced Norm of Matrix?

behzad baghapour behzad.baghapour at gmail.com
Sun Oct 30 11:33:39 CDT 2011

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
Fax: 0098-21-88020741
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