[R] matrix of eigenvalues

Peter Dalgaard p.dalgaard at biostat.ku.dk
Thu Oct 21 22:55:00 CEST 2004

Spencer Graves <spencer.graves at pdf.com> writes:

>       That sounds like what the default method of "mexp" does, though
> I haven't checked it to be sure.  That works fine if the eigenvalue
> part of the Jordan canonical form is diagonal.  That does not hold for
> your examples.  However, the theorem I mentioned from one of Bellman's
> books says that any matrix can be approximated arbitrarily closely
> with another matrix with unique eigenvalues, for which the default
> method of "mexp" seems to work.  For more, see the classic paper by
> Moler and van Loan that Doug mentioned on "Nineteen Dubious Ways to
> Calculate the Matrix Exponential".     hope this helps.     spencer
> graves

An old item on my TODO list is to lift the version of mexp in Octave
into R. As far as I know, that one is just about as robust as they
come. Unfortunately, it is in C++. 

BTW, there's a "Son of 19Dubious" paper, celebrating its 25th
anniversary. I forget its exact coordinates, except that it is from
1978 + 25 = 2003... Someone mentioned it last time the topic came up.

   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

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