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A New Type of Restarted Krylov Methods
Hydrological Service, Jerusalem, Israel
- 1 Hydrological Service, Jerusalem, Israel
Advances in Linear Algebra & Matrix Theory·Volume 07 (2017)·Pages 18–28·Published 15 February 2017·DOI10.4236/alamt.2017.71003
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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.
KeywordsRestarted Krylov MethodsExterior EigenvaluesSymmetric MatricesMonotonicityStarting Vectors
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