A Rational Even-IRA Algorithm for the Solution of $T$-Even Polynomial Eigenvalue Problems
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Bibliographic record
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 [V. Mehrmann, C. Schröder, and V. Simoncini, Linear Algebra Appl., 436 (2012), pp. 4070--4087]. To preserve the structure, a sparse $T$-even linearization from the class of block minimal bases pencils is applied (see [F. M. Dopico et al., Numer. Math., 140 (2018), pp. 373--426). Due to this linearization, the Krylov basis vectors can be computed in a cheap way. Based on the ideas developed in [P. Benner and C. Effenberger, Taiwanese J. Math., 14 (2010), pp. 805--823], 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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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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