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

2020/09/03 by Peter Benner, Heike Faßbender, Benner, Peter +3
Computer Science · Mathematics · Physics and Astronomy · #15A18 #15B57 #65F15 #65F30 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2009.01762

openalex publication_date 2020/09/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

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

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