Numerical comutation of eigensystems?

[Uwe Weber-2]

Hello,

is there a Maxima function for the numerical computation of eigenystems?
The symbolic methods used in the eigenvectors(..) and eigenvalues(..)
functions (as well as in related functions such as jordan or modematrix)
of course usually fail for matrices of order greater than 4.

As for the eigenvalues, I could of course compute allroots of the
charpoly, but this doesn't help much for eigenvectors, since approximate
  eigenvalues result in a trivial nullspace.

Kind regards

Uwe

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[Barton Willis]

-----maxima-bounces@... wrote: -----

>is there a Maxima function for the numerical
>computation of eigenystems?

The linearalgebra package has code for the Jacobi
method, but this method is restricted to real
symmetric matrices. I don't know of any other
numerical code for eigenvalues / vectors. Would you
like to contribute?

(%i1) load(linearalgebra)$
(%i2) m : genmatrix(lambda([i,j],1/(i+j-1)),5,5)$
(%i3) eigens_by_jacobi(m,floatfield);
(%o3) [[1.5670506910982309,0.2085342186110134,3.2879287721665683
*10^-6,0.011407491623419795,
3.0589804015119409*10^-4],

And
(%i4) eigens_by_jacobi(m,bigfloatfield);

Barton
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[Yigal Weinstein]

I feel at my present state of being I must preface each reply I give as,
"I am only an end user".  After such gibberish I will get down to my
point.  Why do you want to use Maxima to Numerically solve anything
non-trivial?  I mean as Octave exists and as far as I know there are
exstensive resources for eigenvalue problems through this software
program, and through many others, trying to use Maxima to solve
eigenvalue problems numerically is like using a sowing needle to bang in
a nail.  That is the needle might do it after some work but its purpose
is far removed from the purpose it is being used for and if you really
want to do that with a needle you might end up braking it ( - this is
not exactly as strong a position as necessary but it is used to make my
point).  

I have had success using Fortran/Octave to numerically crunch
eigenvalues while I used Maxima symbollically to obtain the elements of
the matrices I was interested in finding eigenvalues for.  As a
prejudice I think this is the way to go.  Numerical eigenvalues have
been dealt to with to death in the 60s,70s,80s,90s, why not use what
exists and a lot of it is free, gfortran, C(+,++), Octave, etc., as in
beer and GNU.
 
>is there a Maxima function for the numerical
>computation of eigenystems?
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[Raymond Toy (RT/EUS)]

Uwe Weber wrote:
> Hello,
>
> is there a Maxima function for the numerical computation of eigenystems?
>  
FWIW, I have a partial conversion of LAPACK function dgeev that computes
eigenvalues and eigenvectors for general real matrices.

Would real matrices be good enough?

It's not really ready yet and definitely not integrated with maxima in
any way, but a few simple tests show that it works.

Ray
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