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Re: Any ideas?

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

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.


On 25 Jul 2000 Yannis.Paraskevopoulos at 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
> +44 (0) 20 7568 1865 
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