A Rational Even-IRA Algorithm for the Solution of T-even Polynomial Eigenvalue Problems
| Autor: | Peter Benner, Heike Fassbender, Philip Saltenberger |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Polynomial
MathematicsofComputing_NUMERICALANALYSIS Structure (category theory) Skew TheoryofComputation_GENERAL Numerical Analysis (math.NA) Krylov subspace Base (topology) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis Analysis Eigenvalues and eigenvectors 15A18 15B57 65F15 65F30 Mathematics |
| Zdroj: | SIAM Journal on Matrix Analysis and Applications |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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