Re: Re: MatrixExponential
- To: mathgroup at smc.vnet.net
- Subject: [mg42848] Re: [mg42805] Re: MatrixExponential
- From: Janak Wedagedera <janak at maths.warwick.ac.uk>
- Date: Wed, 30 Jul 2003 19:30:51 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi Jens, Thanks so much for your reply. Yes, that's true. In fact the package 'expokit' (in fortran) (http://www.maths.uq.edu.au/expokit) does this better. With expokit one can compute $\exp(A t).v$ fast enough when A is of order,say, 5000. But I would like to get it done on Mathematica. So, what you are suggesting is instead of using MatrixExp to use the direct method (diagonalization via JordanDecomposition,...) ? Regards Janak. On Wed, 30 Jul 2003, Jens-Peer Kuska wrote: > Hi, > > the MatrixExp[] ist typical computed by the transformation of the > matrix to diagonal form, for a diagonal matrix > the Exp[m] is just the exponetial of the diagonal matrix > with the exponential of th eigenvalues and the matrix is > transformed back to the original basis. > > How ever the eigenvectors (and the transformation matrix) > is usual *not* sparse and Mathematica or any system can help > you ... > > Regards > Jens > > Janak Wedagedera wrote: > > > > Hello, > > > > I am using Mathematica 4.2 on Linux. > > > > I have a question on sparse matrices: > > > > - Is there any way to compute matrix exponential > > (via MatrixExp) for sparse matrices in version > > 4.2 ? It works fine for matrices of order \le 100, > > but I do not know how to use it to compute exp(A t) type > > of thing when A is sparse (band, of order \ge > > 1000). > > > > Thanks in advance, > > Janak. > > ------------------------------------ Dr. Janak R Wedagedera Research Fellow Mathematics Institute University of Warwick Coventry CV4 7AL U.K. e-mail: janak at maths.warwick.ac.uk janak at maths.ruh.ac.lk phone: 44 02476 523698 (office) ------------------------------------