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Any ideas?

• To: mathgroup at smc.vnet.net
• Subject: [mg24591] Any ideas?
• From: Yannis.Paraskevopoulos at ubsw.com
• Date: Tue, 25 Jul 2000 00:56:23 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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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