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Journal Articles Computational Methods in Applied Mathematics Year : 2020

Convergence and Preconditioning of Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

Rayan Nasser
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Abstract

Abstract This paper focuses on the inner iteration that arises in inexact inverse subspace iteration for computing a small deflating subspace of a large matrix pencil. First, it is shown that the method achieves linear rate of convergence if the inner iteration is performed with increasing accuracy. Then, as inner iteration, block-GMRES is used with preconditioners generalizing the one by Robbé, Sadkane and Spence [Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems, SIAM J. Matrix Anal. Appl. 31 2009, 1, 92–113]. It is shown that the preconditioners help to maintain the number of iterations needed by block-GMRES to approximately a small constant. The efficiency of the preconditioners is illustrated by numerical examples.
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Dates and versions

hal-04306747 , version 1 (25-11-2023)

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Rayan Nasser, Miloud Sadkane. Convergence and Preconditioning of Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems. Computational Methods in Applied Mathematics, 2020, 20 (2), pp.343-359. ⟨10.1515/cmam-2018-0212⟩. ⟨hal-04306747⟩
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