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Re: Any ideas?
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 > > > > This message contains confidential information and is intended only > for the individual named. If you are not the named addressee you > should not disseminate, distribute or copy this e-mail. Please > notify the sender immediately by e-mail if you have received this > e-mail by mistake and delete this e-mail from your system. > > E-mail transmission cannot be guaranteed to be secure or error-free > as information could be intercepted, corrupted, lost, destroyed, > arrive late or incomplete, or contain viruses. The sender therefore > does not accept liability for any errors or omissions in the contents > of this message which arise as a result of e-mail transmission. If > verification is required please request a hard-copy version. This > message is provided for informational purposes and should not be > construed as a solicitation or offer to buy or sell any securities or > related financial instruments. > > >