Hi Andrew -
concerning the matrix-exponential and matrixlogarithm...
Are you aware of the article "19 dubious ways to compute the matrix-exponential" of Moler/van Loan? They work out, that the "naive" exponential-series is just one of the poorest selections... (if it is difficult to find online, I cut put a copy on my webspace - I won't attach it here as usual, since it is about 3 MB)
So I didn't expect my own "naive" implementation in Pari/Gp as not really worth to publish, for instance. It should be made explicitely clear for which range of parameters/types of matrices the exponential-series is appropriate. The same is even more true for the matrix-logarithm.
On the other hand, for cases, where the "naive" methods are applicable, I can provide some enhancements - optimization for computation and acceleration of sums using Euler-summation-coefficients. I could send my Pari/Gp-routines for this (or display them here). However, the Euler-summation is not yet "dynamic", which means it doesn't itself evaluate the given matrix-parameter to find the appropriate order but the user must give a guess (and find out the best order by trial&error).
If this would be helpful, please let me know.
Gottfried
concerning the matrix-exponential and matrixlogarithm...
Are you aware of the article "19 dubious ways to compute the matrix-exponential" of Moler/van Loan? They work out, that the "naive" exponential-series is just one of the poorest selections... (if it is difficult to find online, I cut put a copy on my webspace - I won't attach it here as usual, since it is about 3 MB)
So I didn't expect my own "naive" implementation in Pari/Gp as not really worth to publish, for instance. It should be made explicitely clear for which range of parameters/types of matrices the exponential-series is appropriate. The same is even more true for the matrix-logarithm.
On the other hand, for cases, where the "naive" methods are applicable, I can provide some enhancements - optimization for computation and acceleration of sums using Euler-summation-coefficients. I could send my Pari/Gp-routines for this (or display them here). However, the Euler-summation is not yet "dynamic", which means it doesn't itself evaluate the given matrix-parameter to find the appropriate order but the user must give a guess (and find out the best order by trial&error).
If this would be helpful, please let me know.
Gottfried
Gottfried Helms, Kassel