A Contour-integral Based QZ Algorithm for Generalized Eigenvalue Problems

TL;DR

This paper introduces a novel contour-integral based QZ algorithm for efficiently computing selected eigenvalues of generalized eigenvalue problems, improving upon existing contour integral eigensolvers.

Contribution

It develops a new contour-integral based QZ method that enhances eigenpair extraction for generalized problems, extending the CIRR approach with practical implementation strategies.

Findings

Demonstrates effective computation of targeted eigenvalues

Shows improved accuracy over traditional methods

Validates performance through numerical experiments

Abstract

Recently, a kind of eigensolvers based on contour integral were developed for computing the eigenvalues inside a given region in the complex plane. The CIRR method is a classic example among this kind of methods. In this paper, we propose a contour-integral based QZ method which is also devoted to computing partial spectrum of generalized eigenvalue problems. Our new method takes advantage of the technique in the CIRR method of constructing a particular subspace containing the eigenspace of interest via contour integrals. The main difference between our method and CIRR is the mechanism of extracting the desired eigenpairs. We establish the related framework and address some implementation issues so as to make the resulting method applicable in practical implementations. Numerical experiments are reported to illustrate the numerical performance of our new method.