Pitfalls When Solving Eigenproblems - With Applications in Control Engineering

Vasile Sima, Peter Benner

Abstract

There is a continuous research effort worldwide to improve the reliability, efficiency, and accuracy of numerical computations in various domains. One of the most promising research avenues is to exploit the structural properties of the mathematical problems to be solved. This paper investigates some numerical algorithms for the solution of common and structured eigenproblems, which have many applications in automatic control (e.g., linear-quadratic optimization and H¥-optimization), but also in various areas of applied mathematics, physics, and computational chemistry. Of much interest is to find the eigenvalues and certain deflating subspaces, mainly those associated to the stable eigenvalues. Several simple examples are used to highlight the pitfalls which may appear in such numerical computations, using state-of-the-art solvers. Balancing the matrices and the use of condition numbers for eigenvalues are shown to be essential options in investigating the behavior of the solvers and problem sensitivity.

References

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Paper Citation


in Harvard Style

Sima V. and Benner P. (2015). Pitfalls When Solving Eigenproblems - With Applications in Control Engineering . In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-122-9, pages 171-178. DOI: 10.5220/0005533301710178


in Bibtex Style

@conference{icinco15,
author={Vasile Sima and Peter Benner},
title={Pitfalls When Solving Eigenproblems - With Applications in Control Engineering},
booktitle={Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2015},
pages={171-178},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005533301710178},
isbn={978-989-758-122-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Pitfalls When Solving Eigenproblems - With Applications in Control Engineering
SN - 978-989-758-122-9
AU - Sima V.
AU - Benner P.
PY - 2015
SP - 171
EP - 178
DO - 10.5220/0005533301710178