Spectral analysis of sparse symmetric integer matrices - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T00:39:09Z http://mathoverflow.net/feeds/question/71866 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/71866/spectral-analysis-of-sparse-symmetric-integer-matrices Spectral analysis of sparse symmetric integer matrices guidupuy 2011-08-02T09:16:46Z 2011-08-02T13:42:56Z <p>Hi all,</p> <p>A project I'm currently working on requires me to compute the eigenvectors / eigenvalues of sparse symmetric integer matrices. This is needed in the context of Principal Component Analysis. I tried to look around for efficient algorithms but am not 100% sure where to start.</p> <p>Ideally, I'd like to find the first 10 eigenvectors (e.g. corresponding to the 10 biggest eigen values) of a 10k x 10k matrix in less than 10 seconds.</p> <p>Is that a crazy objective? What property of the matrices would you leverage? Integer + symmetric screams Smith Normal Form but I'm wondering if there exists better than that...</p> <p>Any help appreciated! Thanks in advance,</p> <p>Guillaume </p> http://mathoverflow.net/questions/71866/spectral-analysis-of-sparse-symmetric-integer-matrices/71881#71881 Answer by Federico Poloni for Spectral analysis of sparse symmetric integer matrices Federico Poloni 2011-08-02T13:42:56Z 2011-08-02T13:42:56Z <p><a href="http://www.caam.rice.edu/software/ARPACK/" rel="nofollow">http://www.caam.rice.edu/software/ARPACK/</a> is the standard tool. It's Fortran (ouch), but there are libraries to call it from C++, Matlab, Python, and possibly also other languages that I do not know (I'd be surprised if there were no Java adapter around, for instance).</p> <p>Don't write your restarted Arnoldi implementation from scratch if you have no previous experience in numerical analysis, it might be tricky.</p>