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

2017/08/28 by Andrew Knyazev, Knyazev, Andrew · 1 citation
Computer Science · Engineering · Physics and Astronomy · #65F15 #Advanced Numerical Methods in Computational Mathematics #Computation (stat.CO) #Electromagnetic Scattering and Analysis #FOS: Computer and information sciences #FOS: Mathematics #G.1.3 #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1708.08354

openalex publication_date 2017/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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