[SciPy-dev] Re: [SciPy-user] Matrix square root

Nils Wagner 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.
>
>
Travis,

Again, Higham is a source for this issue.
http://www.ma.man.ac.uk/~higham/talks/
How and how not to compute the matrix square root (1997)

Also published in

Numerical Algorithms
*15* (2): 227-242, 1997
/Copyright © 1997 Kluwer Academic Publishers/
/All rights reserved/


    Stable iterations for the matrix square root


Nils

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