TITLE:
A New Type of Restarted Krylov Methods
AUTHORS:
Achiya Dax
KEYWORDS:
Restarted Krylov Methods, Exterior Eigenvalues, Symmetric Matrices, Monotonicity, Starting Vectors
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.7 No.1,
March
31,
2017
ABSTRACT: In this paper we present a new type of Restarted Krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process, and the use of polynomial filtering. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the eigenvalues toward their limits. The Krylov matrices that we use lead to fast rate of convergence. Numerical experiments illustrate the usefulness of the proposed approach.