Hi thanks for the responses, Jose, I switched to the EPS approach that you suggested but am having difficulties with convergence, once i move beyond some basic test matrices.
I'm trying to put together a basic test which might help some I'll post it once i get it together. Thanks again -Luke On 07/07/2010 12:33 PM, Jose E. Roman wrote: > On 07/07/2010, Luke Bloy wrote: > > >> Hi, >> >> First off I apologize for the slepc question, they don't have a users lists >> so I'm hoping someone on here might be able to offer some guidance. >> >> Problem: >> I'm working on a graph partitioning problem. Basically I have the laplacian >> of a large graph and am interested in extracting its connected sub >> components. An approach is to compute the smallest eigenvalues and >> eigenvectors of the laplacian matrix. it is known that the lowest eigenvalue >> of the laplacian is 0, and has a multiplicity of K if the graph has K >> subcomponents. These subcomponents can be extracted from the smallest >> eigenvectors. >> >> Question: >> What is the best approach within slepc to attack this problem? >> >> I've been using SVD solvers using the LANCOS method to attack this problem, >> but sometimes have convergence problems. I know one of the smallest eigen >> vectors is the vector of all ones, and have tried to initialize the svd >> solver with this vector but this has led to very strange problems. >> >> Would I be better off using one of the EPS solvers? If so which can >> correctly extract multiplicities of eigenvalues? >> >> Thanks, >> Luke >> > SLEPc's example 11 > (http://www.grycap.upv.es/slepc/documentation/current/src/examples/ex11.c.html > ) computes the Fiedler vector of a graph, i.e., the second eigenvector of > the Laplacian (assuming a connected graph). > > The example uses EPS because for symmetric (semi-)definite matrices the > singular value decomposition is equal to the eigendecomposition. > > In your case, you want to explicitly compute the eigenspace associated to the > zero eigenvalue. Then you can simply use ex1.c choosing the smallest > eigenvalues (e.g. with the flag -eps_smallest_real). The default EPS solver > (Krylov-Schur) shouldn't have any problems with multiple zero eigenvalues. > > If you can't get it work, contact us at the slepc-maint email address. > > Regards, > Jose > >
