bo198214 Wrote:I come to the same formula, however computing indexes above 15 is nearly impossible. So it seems that your methods somehow are faster than the direct double binomial expansion executed in Maple.
Whats your biggest index (say it takes below 5min) that you can compute and by which method on which system?
Hmm, with dimension = 64 , let it come to 1 minute for the computations of that matrix-exponential with the variable n.
[update:]
Just tried with dim=32, it was, let's say 2 seconds. (So the above guess was a bit rough... ;-) )
[/update]
Usually I calculate with dim=32 and can be in a reasonable dialog with the system, so less a second to some seconds.
If I compute eigensystems I had longer computation times, assumably because of required higher precision (my default is 80 or 200 digits float, with eigensystem analysis I needed sometimes 800 digits with dim=32) and for such analyses I wait possibly some minutes. My application is Pari/GP, btw.
In the german math-newsgroup some readers provided me with results for crosscheck and mentioned, they were able to do such eigenanalyses with mathematica or maple up to dimension =128 in some seconds or few minutes - don't know how this difference is possible (I even didn't try the eigenanalysis with dim=64 in my Pari/GP-setting).
Gottfried
Ah, well, the system: 1 GHz CPU, 1 GByte Ram, Win Xp
Pari/Gp interfaced by my Pari-TTY-Gui
[edit 2]
Actually, with nilpontent matrices I use the simpler formula, given M
F=matid(dim);S=F;
for(k=1,dim,
F = F*M/k ; S = S + F )
[/edit 2]
Gottfried Helms, Kassel
