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arXiv · 2009.01762

A rational Even-IRA algorithm for the solution of T-even polynomial eigenvalue problems

Peter Benner·Heike Fassbender·Philip Saltenberger
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Abstract

In this work we present a rational Krylov subspace method for solving real large-scale polynomial eigenvalue problems with T-even (that is, symmetric/skew-symmetric) structure. Our method is based on the Even-IRA algorithm. To preserve the structure, a sparse T-even linearization from the class of block minimal bases pencils is applied. Due to this linearization, the Krylov basis vectors can be computed in a cheap way. A rational decomposition is derived so that our method explicitly allows for changes of the shift during the iteration. This leads to a method that is able to compute parts of the spectrum of a T-even matrix polynomial in a fast and reliable way.

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Peter Benner, Heike Fassbender, Philip Saltenberger. 2020-09-03. A rational Even-IRA algorithm for the solution of T-even polynomial eigenvalue problems. https://arxiv.org/abs/2009.01762

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