A long time ago I did numerical eigenvalue computations using SLEPC ( see http://www.grycap.upv.es/slepc/ ) There is also Trilinos/Anazazi (I did't use it)
But I was only interested in a part of the spectrum (smallest /largest), Do you need to compute all eigenvalues? Maybe (as William said) you should look for available software. I know about the following existing survey: http://www.grycap.upv.es/slepc/documentation/reports/str6.pdf Jakob Am Samstag, 13. September 2014 20:53:50 UTC+2 schrieb wstein: > > On Sat, Sep 13, 2014 at 11:28 AM, Erik Slivken > <> wrote: > > William- > > > > I am trying to find the eigenvalues of a roughly 10000x10000 sparse > matrix > > with entries from {0,1} (and would like to do this for even larger > > matrices). I don't know what could be done to increase the speed (right > now > > it has been running for roughly half a day). But it said to email you > to > > raise a quota. Also, if there is special faculty access, this is a > project > > with Chris Hoffman from UW and I am sure he would sign on for more > computing > > power. > > > > Thanks for your time. > > > > Cheers, > > Erik Slivken > > > > P.S. How long should it take to find the eigenvalues of a 10000x10000 > > sparse matrix with entries from {0,1}? What about a 10^6x10^6 sparse > matrix > > with entries in from {0,1}? > > Never. Sage doesn't have any easily available sophisticated sparse > linear algebra algorithms, as far as I know. Linbox (which is in Sage > -- a C++ library), might have something; and Cremona's eclib has some > gems hidden in it. I wrote some really stupid sparse linear algebra, > which was sufficient for something I did once. There's several > stages to sparse algorithms, and what is in Sage only implements the > first part -- the "endgame", which is to solve a resulting dense > system at a certain point, isn't in sage. Sebastian Pancratz and I > did implement it once > somewhere... (not sure), but it isn't in sage (and it was not easy), > and now Sebastian works at a bank. > > Try typing > > set_verbose(2) > > to see what is happening, if you're using sage. > > You should seriously consider searching the web for current available > software for sparse linear algebra. Last I checked, unfortunately, > Sage is definitely not an off-the-shelf solution for anything > nontrivial involving sparse matrices, except for maybe efficiently > storing them. > > (I've changed the subject and cc'd some people on this email, in case > anybody knows anything about sparse linear algebra and wants to chime > in.) > > William > > -- > William Stein > Professor of Mathematics > University of Washington > http://wstein.org > [email protected] <javascript:> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
