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

TL;DR

This paper introduces a rational Krylov subspace method based on the Even-IRA algorithm for efficiently solving large-scale T-even polynomial eigenvalue problems while preserving their structure.

Contribution

It develops a structure-preserving rational Krylov method using sparse linearizations and allows shift changes during iteration for improved spectrum computation.

Findings

Efficient computation of spectrum parts for T-even polynomials.

Structure preservation via block minimal bases pencils.

Flexible shift strategy enhances convergence.

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.