Computing eigenpairs in augmented Krylov subspace produced by Jacobi–Davidson correction equation

Abstract

In this paper, we present an augmented Krylov subspace method for computing some extreme eigenvalues and corresponding eigenvectors of Hermitian matrices. The augmented Krylov subspace, which is a union of the standard Krylov subspace and another low-dimension subspace used to extract the approximations to the desired eigenpairs, is essentially different from the projection subspace involved in the Jacobi–Davidson iteration method. The augmented Krylov subspace method converges globally and attains cubic convergence rate locally. Some numerical experiments are carried out to demonstrate the convergence property and the competitiveness of this method.