On Relaxed Filtered Krylov Subspace Method for Non-Symmetric Eigenvalue Problems

TL;DR

This paper introduces a novel relaxed filtered Krylov subspace method for efficiently computing dominant eigenvalues of non-symmetric matrices, with theoretical analysis and numerical validation demonstrating its robustness and superiority.

Contribution

The paper proposes a new relaxed filtered Krylov subspace method and generalizes existing methods, providing convergence analysis and demonstrating improved performance over current techniques.

Findings

The method effectively computes eigenvalues with large real parts.

Numerical experiments show the method's robustness and superiority.

Convergence analysis supports the method's theoretical foundation.

Abstract

In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric matrices. As by-products, the generalizations of the filtered Krylov subspace method and the Chebyshev-Davidson method for solving non-symmetric eigenvalue problems are also presented. We give the convergence analysis of the complex Chebyshev polynomial, which plays a significant role in the polynomial acceleration technique. In addition, numerical experiments are carried out to show the robustness of the relaxed filtered Krylov subspace method and its great superiority over some state-of-the art iteration methods.