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Journal Articles Computational Methods in Applied Mathematics Year : 2022

Inexact Inverse Subspace Iteration with Preconditioning Applied to Quadratic Matrix Polynomials

Abstract

Abstract An inexact variant of inverse subspace iteration is used to find a small invariant pair of a large quadratic matrix polynomial. It is shown that linear convergence is preserved provided the inner iteration is performed with increasing accuracy. A preconditioned block GMRES solver is employed as inner iteration. The preconditioner uses the strategy of “tuning” which prevents the inner iteration from increasing and therefore results in a substantial saving in costs. The accuracy of the computed invariant pair can be improved by the addition of a post-processing step involving very few iterations of Newton’s method. The effectiveness of the proposed approach is demonstrated by numerical experiments.
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Dates and versions

hal-04306765 , version 1 (25-11-2023)

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Cite

Miloud Sadkane. Inexact Inverse Subspace Iteration with Preconditioning Applied to Quadratic Matrix Polynomials. Computational Methods in Applied Mathematics, 2022, 22 (1), pp.181-197. ⟨10.1515/cmam-2020-0175⟩. ⟨hal-04306765⟩
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