Preconditioned inexact Jacobi–Davidson method for large symmetric eigenvalue problems

Abstract

A preconditioned inexact Jacobi-Davidson method for the computation of the eigenpairs of large and sparse symmetric matrices is proposed. In each inner iteration step of Jacobi-Davidson method, two preconditioners based on a regularization method and shift-splitting of the saddle point matrix are given. Then the properties of the preconditioned matrix are investigated. Numerical results illustrate that the new proposed algorithms are more efficient than Jacobi-Davidson method.