Deflation by restriction for the inverse-free preconditioned Krylov subspace method

Qiao  Liang; Qiang  Ye

doi:10.3934/naco.2016.6.55

Article Contents

2016, Volume 6, Issue 1: 55-71. Doi: 10.3934/naco.2016.6.55

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Deflation by restriction for the inverse-free preconditioned Krylov subspace method

Qiao Liang^1, and
Qiang Ye^1,

1.
Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027

Received: June 2015

Revised: December 2015

Published: December 2015

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Abstract

A deflation by restriction scheme is developed for the inverse-free preconditioned Krylov subspace method for computing a few extreme eigenvalues of the definite symmetric generalized eigenvalue problem $Ax = \lambda Bx$. The convergence theory for the inverse-free preconditioned Krylov subspace method is generalized to include this deflation scheme and numerical examples are presented to demonstrate the convergence properties of the algorithm with the deflation scheme.

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Mathematics Subject Classification: Primary: 65F15.

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