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2016, 6(1): 55-71. doi: 10.3934/naco.2016.6.55

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

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

Received  June 2015 Revised  December 2015 Published  January 2016

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.
Citation: Qiao Liang, Qiang Ye. Deflation by restriction for the inverse-free preconditioned Krylov subspace method. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 55-71. doi: 10.3934/naco.2016.6.55
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##### References:
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