Recent implementations, applications, and extensions of the Locally Optimal Block Preconditioned Conjugate Gradient method (LOBPCG)

TL;DR

This paper reviews recent developments, implementations, and applications of the LOBPCG method, highlighting its versatility and extensions beyond standard eigenvalue problems in various scientific fields.

Contribution

It provides a comprehensive overview of recent advancements and new extensions of the LOBPCG method in computational science.

Findings

LOBPCG has been successfully applied in mechanics, material sciences, and data sciences.

Recent implementations have improved efficiency and scalability.

Extensions of local optimality have broadened the method's applicability.

Abstract

Since introduction [A. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SISC (2001) DOI:10.1137/S1064827500366124] and efficient parallel implementation [A. Knyazev et al., Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in HYPRE and PETSc, SISC (2007) DOI:10.1137/060661624], LOBPCG has been used is a wide range of applications in mechanics, material sciences, and data sciences. We review its recent implementations and applications, as well as extensions of the local optimality idea beyond standard eigenvalue problems.