A Robust and Efficient Implementation of LOBPCG.

Abstract

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely\nused to compute eigenvalues of large sparse symmetric matrices. The algorithm\ncan suffer from numerical instability if it is not implemented with care. This\nis especially problematic when the number of eigenpairs to be computed is\nrelatively large. In this paper we propose an improved basis selection strategy\nbased on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence\ncriterion which is backward stable to enhance the robustness. We also suggest\nseveral algorithmic optimizations that improve performance of practical LOBPCG\nimplementations. Numerical examples confirm that our approach consistently and\nsignificantly outperforms previous competing approaches in both stability and\nspeed.\n