It's apparently already been pointed out that the paper Chris is probably remembering is this one: C. Moler and C. Van Loan. Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev., 20(4):801-836, 1978. But a bit of finagling reveals that they've written a recapitulation, now available on the intertoobz: C. Moler and C. Van Loan. Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later SIAM Rev., 45(1):3-49, 2003. http://www.cs.cornell.edu/cv/ResearchPDF/19ways+.pdf Abstract. In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency indicates that some of the methods are preferable to others, but that none are completely satisfactory. Most of this paper was originally published in 1978. An update, with a separate bibliography, describes a few recent developments.
Date: Thu, 17 May 2007 09:16:42 -0700 (PDT) From: Eugene Salamin <gene_salamin@yahoo.com>
Curve fitting and parameter estimation are applications of Bayesian methodology. Have a look at http://bayes.wustl.edu/ and in particular the publications of Larry Bretthorst. Several of them have titles suggesting their relevance to your problem.
----- Original Message ---- From: Chris Landauer <cal@rush.aero.org> To: math-fun@mailman.xmission.com
i remember a paper from one of the siam journals (probly numerical methods or something) from many years ago whose title was something like how not to fit an exponential
the author(s?) describe i think 20 ways that are plausible, but do not work, and explain what the ill-conditioning means and even why (or at least that) it happens a lot
i've run into this fitting some laser data to the energy transfer equations between different levels of different rare earths (not my problem, my favorite physicist friend's problem; she does the experiments and gets LOTSA data)
-- Steve Rowley <sgr@alum.mit.edu> http://alum.mit.edu/www/sgr/ Skype: sgr000