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Re: Jacobi Matrix Exponential

• To: mathgroup at smc.vnet.net
• Subject: [mg39714] Re: Jacobi Matrix Exponential
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Mon, 3 Mar 2003 23:48:41 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <b3pg0e$7dk$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

the standard eigenvalue algorithm transforms the matrix to
tridagonal form, that you alread have. Have a look at

http://www.library.cornell.edu/nr/bookcpdf/c11-3.pdf

but it is still an n^2 process and I assume, that you
have to spend the time to comput the eigenvalues/eigenvectors

Regards
  Jens

Kyriakos Chourdakis wrote:
> 
> Dear all,
> 
> I have to compute matrix exponentials of complex
> matrices. The matrices are quite large, e.g. up to
> 1000x1000, but only the diagonal and the adjacent
> elements are non zero. The first and last rows are
> zero. The matrix is therefore of the form [x denotes a
> non-zero complex element, not all x's are the same]:
> 
> 0 0 0 0 0 0 0 .....
> x x x 0 0 0 0 .....
> 0 x x x 0 0 0 .....
> 0 0 x x x 0 0 .....
> 0 0 0 x x x 0 .....
> . . . . . . .
> . . . . . . .
> 
> Does anyone have in mind, or has experimented with, a
> quick way of computing such exponentials. The built-in
> function is very slow.
> 
> My experiments with Pade approximations include matrix
> inversion and are therefore slow as well. Perhaps a
> quick way of inverting such matrices would also be
> helpful.
> 
> Best,
> 
> Kyriakos
> 
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