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Given a matrix I want to evaluate $e^{A}$. The method suggested uses the taylor expansion. But, it is also written that the method works well if the largest and smallest eigen values are not well separated. why ?

Anonymous
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  • see http://www.cs.cornell.edu/cv/researchpdf/19ways+.pdf – Will Jagy Oct 25 '14 at 04:37
  • @WillJagy: That's a little dubious :-). – copper.hat Oct 25 '14 at 04:55
  • @copper.hat: Why should this paper be dubious? Note that Cleve Moler has built the first version of Matlab. – Christian Blatter Oct 25 '14 at 11:56
  • @ChristianBlatter: It was a joke. The original paper was titled something like "19 dubious ways to compute the exponential". I used to work with the old (free) Fortran version of Matlab which even had the rtfm command. – copper.hat Oct 25 '14 at 15:44
  • @copper.hat, I never read it, it is in one of the comments after my http://math.stackexchange.com/questions/80324/sina-where-a-is-a-matrix/80332#80332 a little after the gerbils – Will Jagy Oct 25 '14 at 16:24
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    @WillJagy: Funny! (Btw, I think the gerbils might find a Schur form to be preferable to the Jordan normal form from a numerical standpoint...) – copper.hat Oct 25 '14 at 16:34

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