[SciPy-dev] Re: [SciPy-user] Matrix square root
nwagner at mecha.uni-stuttgart.de
Tue Oct 5 05:30:46 CDT 2004
Travis Oliphant wrote:
> Pearu Peterson wrote:
>> On Mon, 4 Oct 2004, Nils Wagner wrote:
>>> AFAIK there is no direct support for sqrtm but you may use funm.
>> I just discovered that there might be a bug in funm. I have added
>> a test to scipy.linalg.test_matfuncs that demonstrates the bug.
>> So, be aware to check the results of funm(..,sqrt).
> As far as I undertand, the idea of a general purpose matrix function
> has precision problems. The algorithm in scipy is based on a
> published algorithm using the Schur decomposition. That is why it is
> usually a good idea to write separate algorithms for special matrix
> functions if possible.
> Is this really a bug, or just a problem with using the generic funm
> algorithm when a more accurate algorithm exists.
> The fact that you can return a reasonable square root for non-special
> matrices makes me believe that it is not a bug in funm, but a
> demonstration that the generic funm algorithm does not always produce
> the best results for specific functions of matrices.
> -Travis O.
Again, Higham is a source for this issue.
How and how not to compute the matrix square root (1997)
Also published in
*15* (2): 227-242, 1997
/Copyright © 1997 Kluwer Academic Publishers/
/All rights reserved/
Stable iterations for the matrix square root
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