Improving the Convergence of the Periodic QZ Algorithm

Vasile Sima, Pascal Gahinet

2019

Abstract

The periodic QZ algorithm involved in the structure-preserving skew-Hamiltonian/Hamiltonian algorithm is investigated. These are key algorithms for many applications in diverse theoretical and practical domains such as periodic systems, (robust) optimal control, and characterization of dynamical systems. Although in use for several years, few examples of skew-Hamiltonian/Hamiltonian eigenproblems have been discovered for which the periodic QZ algorithm either did not converge or required too many iterations to reach the solution. This paper investigates this rare bad convergence behavior and proposes some modifications of the periodic QZ and skew-Hamiltonian/Hamiltonian solvers to avoid nonconvergence failures and improve the convergence speed. The results obtained on a generated set of one million skew-Hamiltonian/Hamiltonian eigenproblems of order 80 show no failures and a significant reduction (sometimes of over 240 times) of the number of iterations.

Paper Citation

in Harvard Style

Sima V. and Gahinet P. (2019). Improving the Convergence of the Periodic QZ Algorithm.In Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-380-3, pages 261-268. DOI: 10.5220/0007876902610268

in Bibtex Style

@conference{icinco19,
author={Vasile Sima and Pascal Gahinet},
title={Improving the Convergence of the Periodic QZ Algorithm},
booktitle={Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2019},
pages={261-268},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007876902610268},
isbn={978-989-758-380-3},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Improving the Convergence of the Periodic QZ Algorithm
SN - 978-989-758-380-3
AU - Sima V.
AU - Gahinet P.
PY - 2019
SP - 261
EP - 268
DO - 10.5220/0007876902610268