On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems

Preconditioned Krylov Subspace Methods for Eigenvalue Problems

An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems

In this paper, we present an inverse free Krylov subspace method for nding some extreme eigenvalues of the symmetric de nite generalized eigenvalue problem Ax = Bx. The basic method takes a form of inner-outer iterations and involves no inversion of B or any shift-and-invert matrix A 0B. A convergence analysis is presented that leads to a preconditioning scheme for accelerating convergence thro...

A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems

Relaxed Krylov subspace approximation

Recent computational and theoretical studies have shown that the matrix-vector product occurring at each step of a Krylov subspace method can be relaxed as the iterations proceed, i.e., it can be computed in a less exact manner, without degradation of the overall performance. In the present paper a general operator treatment of this phenomenon is provided and a new result further explaining its...

Eigenvalue Perturbation and Generalized Krylov Subspace Method

In this paper, we study the computational aspect of eigenvalue perturbation theory. In previous research, high order perturbation terms were often derived from Taylor series expansion. Computations based on such an approach can be both unstable and highly complicated. We present here with an approach based on the diierential formulation of perturbation theory where the high order perturbation c...