The computed matrix exponential has huge elements. Note that the elements of A range over 18 orders of magnitude. A Query from a UserĪ few weeks ago, MathWorks Tech Support received a query from a user about the following matrix. The current version of expm in MATLAB is Nick's implementation of scaling and squaring.Ī more recent review of Nick's work on the matrix exponential is provided by these slides for a talk he gave at a meeting in Rome in 2008.
MATLAB EXPONENTIAL PDF
A PDF is available from the University of Manchester's web site. Nick did a careful error analysis of scaling and squaring, improved the efficiency of the algorithm, and wrote a paper for the SIAM Journal on Numerical Analysis, "The scaling and squaring method for the matrix exponential revisited". Our colleague Nick Higham reconsided the matrix exponential in 2005. A PDF is available from Charlie's web site. The SIAM Review paper proved to be very popular and in 2003 we published a followup, "Nineteen Dubious Ways. This was about the time I was tinkering with the first MATLAB and consequently every version of MATLAB has had an expm function, based on scaling and squaring. The paper does not pick a "best of the 19", but cautiously suggests that the "scaling and squaring" algorithm might be OK.
In 1978, Charlie Van Loan and I published a paper in SIAM Review entitled "Nineteen Dubious Ways to Compute the Exponential of a Matrix".
Scaling, Squaring, and Pade Approximations.
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