Date: May 24, 2010 8:37 PM
Author: luca
Subject: Computation of the matrix exponential
Hi,

i have the following problem: given a 3x3 real matrix, compute exp(A).

I need a really fast way to do this. I have searched a bit with

google, but it seems to me that

computing the matrix exponential is not so simple, at least if your

matrix does not have a special

structure (for example A=diagonal matrix).

I have found a simple method that use the diagonalization of A. If A

has 3 distinct eigenvalues, than compute

A=PDP^-1, where P is the matrix of the eigenvectors, D is a diagonal

matrix (whose diagonal elements are

the eigenvalues of A). Than, exp(A) = P exp(D) P^-1. Since P^-1 is

fast enough and exp(D) is simple

to compute, this should be a fast method.

But, the problem is: i am not sure that the matrix A will always have

3 distinct eigenvalues...what happens

if this does not happen? Can i use that formula even if 2 (or all

three) eigenvalues are equal?

Are there any other ways to compute exp(A) in a fast way?

Thank you,

Luca