Thick-restarted joint Lanczos bidiagonalization for the GSVD

Abstract

The computation of the partial generalized singular value decomposition (GSVD) of large-scale matrix pairs can be approached by means of iterative methods based on expanding subspaces, particularly Krylov subspaces. We consider the joint Lanczos bidiagonalization method, and analyze the feasibility of adapting the thick restart technique that is being used successfully in the context of other linear algebra problems. Numerical experiments illustrate the effectiveness of the proposed method. We also compare the new method with an alternative solution via equivalent eigenvalue problems, considering accuracy as well as computational performance. The analysis is done using a parallel implementation in the SLEPc library.