polyvalm problems for defective matrix input

[Rolf Fabian]

Some of Octave's square matrix functions like 'logm' and 'polyvalm'
have the problem that they do not correctly recognize defective
matrix input and consequently their output may differ essentially
from expectation.

Attached zip-file contains an excerpt from AdLA (Advanced Linear
Algebra) package which I started to develop in 1997.

There are 3 m-files included :
'polyvalmh.m' 
'isnormal.m'                 ( auxilliary function )
'polyvalmh_demo.m'

All script functions are heavily commented
and 'polyvalmh' provides two optional switches
'verb' and 'warn' which I've activated prior
to upload in order to increase verbosity.

If you are interested in the topic and like to see
several examples where Octave's output from
'polyvalm' is significantly in error, please run
something like:
'[y_Octave, y_AdLA] = polyvalmh_demo ( N )'
where N = 1, 2, .... 13 .

If the demos convince you that 'polyvalmh.m'
(incl. auxilliary function 'isnormal.m') represent
a better approach to matrix polynomial
evaluation than the currently used 'polyvalm.m',
you might rename and implement it into Octave,
as long as the copyright notice is retained.

May be somebody can check the examples
also against MatLab, which is not available
for me.

Rolf Fabian

< r dot fabian at jacobs-university dot de > 

 

http://www.nabble.com/file/p15183200/AdLA_polyvalmh.zip AdLA_polyvalmh.zip 

-----
Rolf Fabian
<r dot fabian at jacobs-university dot de>

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