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Jacobi Matrix Exponential


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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