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A Rational Even-IRA Algorithm for the Solution of T-Even Polynomial Eigenvalue Problems

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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Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.42 No.3 July-September 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1172-1198

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

KRYLOV SUBSPACE METHOD
RATIONAL KRYLOV DECOMPOSITION
POLYNOMIAL EIGENVALUE PROBLEM
SYMMETRIC/SKEW-SYMMETRIC MATRIX POLYNOMIAL
STRUCTURE-PRESERVING LINEARIZATION

Info Detail Spesifik

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Pernyataan Tanggungjawab

Peter Benner, Heike Fassbender, Philip Saltenberger

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