Thick-restarted joint Lanczos bidiagonalization for the GSVD

TL;DR

This paper introduces a thick-restarted joint Lanczos bidiagonalization method for efficiently computing the partial GSVD of large matrices, improving convergence and computational performance.

Contribution

The paper adapts the thick restart technique to the joint Lanczos bidiagonalization method for GSVD, demonstrating its effectiveness through numerical experiments.

Findings

Enhanced convergence with thick restart technique

Improved computational efficiency over existing methods

Successful parallel implementation in SLEPc

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.