Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method

Numerical solution of extremely large and ill conditioned eigenvalue problems is attracting a growing attention recently as such problems are of major importance in applications. They arise typically as discretization of continuous models described by systems of partial differential equations (PDE’s). For such problems, preconditioned matrix-free eigensolvers are especially effective as the stiffness and the mass matrices do not need to be assembled, but instead can be only accessed through functions of the corresponding vector-matrix products.