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Re: Any ideas?

• To: mathgroup at smc.vnet.net
• Subject: [mg24616] Re: Any ideas?
• From: Erich Mueller <emuelle1 at uiuc.edu>
• Date: Fri, 28 Jul 2000 17:23:53 -0400 (EDT)
• Organization: University of Illinois at Urbana-Champaign
• References: <8lj8t1$8ru@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

The simplest way is to use the Mathematica function MatrixExp.

A nice trick is that if you know the charactaristic polynomial for 
(A+ IB), you can use it to simplify the Taylor series that you wrote down.

Erich

On 25 Jul 2000 Yannis.Paraskevopoulos at ubsw.com wrote:

> Dear All,
> 
> I am working on Fourier transforms, and therefore I want to evaluate
> the exponential of a matrix, say
> z=exp(A+iB). The matrices A and B do not commute, hence (I guess!) the
> exponential cannot be split into real and imaginary parts explicitly.
> Equivalently, I could be looking for the eigenvalues and eigenvectors
> of the matrix A+iB; the exponential is then calculated trivially.
> 
> I have tried the Taylor expansion exp(A+iB)=sum([A+iB]^n/n!,n=0..Inf),
> but the numerical errors become explosive very quickly.
> 
> I would appreciate any clever trick!
> 
> regards
> 
> 
> Yannis Paraskevopoulos
> 
> Quantitative Risk: Models and Statistics
> UBS Warburg, 
> 1st Floor, 
> 1 Finsbury Ave., 
> London EC2M 2PP.
> 
> yannis.paraskevopoulos at ubsw.com
> +44 (0) 20 7568 1865 
> 
> 
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