Recent implementations, applications, and extensions of the Locally Optimal Block Preconditioned Conjugate Gradient method (LOBPCG)
For researchers and practitioners in computational science and engineering, this review consolidates the state of the art of LOBPCG, but is incremental as it does not introduce new results or benchmarks.
This paper reviews recent implementations, applications, and extensions of the LOBPCG method, a preconditioned eigensolver, across mechanics, material sciences, and data sciences. It highlights the method's widespread adoption and discusses extensions beyond standard eigenvalue problems.
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.