Fast Computation of Eigenvectors of a Sparse Matrix

Question

I am working on a project that involves the computation of the eigenvectors of a very large sparse matrix. To be more specific I have a Matrix that is the laplacian of a big graph and I am interested in finding the eigenvector associated to the second smallest eigenvalue. Of course Matlab takes ages to compute the eigenvectors, even because it computes all of them. Any suggestions? Thank you very much Andrea

Answer 1

Have you tried this usage of eigs :

[v,c]=eigs(A,2,'sm');

for example:

A = delsq(numgrid('C',256));  
[v,c]=eigs(A,2,'sm');

generates a ~50K x 50K sparse matrix and find its 2 smallerst eigenvalues and eigenvectors in about 1 second in my old laptop...