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Re: logm robustness
From: |
Philip Nienhuis |
Subject: |
Re: logm robustness |
Date: |
Tue, 20 Apr 2010 12:24:59 -0800 (PST) |
Tommy Guy <guyrt7 at ****> wrote:
> Yes - I agree that a citation is needed. That is why I am questioning
> the comment in the logm and sqrtm methods.
>
> Found a citation that mentions Schur methods as superior
>
> http://eprints.ma.man.ac.uk/156/01/covered/MIMS_ep2006_13.pdf
>
> This paper also has an answer to the question of what kind of matrices
> are unstable.
>
> Richard T. Guy
>
> 2010/4/20 Jordi GutiƩrrez Hermoso <address@hidden>:
>> On 19 April 2010 20:26, Tommy Guy <address@hidden> wrote:
>>> logm is using eigenvalues, which was listed as lacking robustness.
>>
>> [citation needed]
I see that logm.m uses more or less the same basic strategy that funm.m uses
(octave-forge in the linear-algebra-<version> package).
There's an old discussion relating to this on bug-octave archives from 2001
about funm.m (that I contributed) which is very basic and suffers from
probably the same issues.
See:
http://www.octave.org/old-list-archives/bug-octave/2001/64
"numerical artifacts by defective input to matrix functions" and follow-up
posts.
I made funm.m and use(d) it only for my field of expertise where the
relevant matrices are always diagonizable - so for me It Just Works.
Nevertheless funm.m should be improved too in similar fashion as logm.m to
be more widely useful.
I'm no mathematician however so I can't contribute much further.
FWIW I once found a better alternative invoking Schur, but as jwe pointed
out, that alternative might have been pirated from the competition, see
http://www.octave.org/old-list-archives/help-octave/2004/760
Another alternative may be to check how scilab does their collection of
matrix functions and borrow from them - scilab's license permitting. But
IIRC (it's many years ago that I had a look at their docs) scilab's matrix
functions are fairly basic too.
Philip
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