  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.
