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 > > __________________________________________________ > Do You Yahoo!? > Everything you'll ever need on one web page > from News and Sport to Email and Music Charts > http://uk.my.yahoo.com