Constructive Analysis of Eigenvalue Problems in Control under Numerical Uncertainty

The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or Jordan normal forms. Perturbation theory and various regulariza...

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Vydáno v:International journal of control, automation, and systems Ročník 18; číslo 9; s. 2177 - 2185
Hlavní autoři: Osinenko, Pavel, Devadze, Grigory, Streif, Stefan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.09.2020
Springer Nature B.V
제어·로봇·시스템학회
Témata:
Canonical forms
Computation
Control
Control methods
Eigenvalues
Eigenvectors
Engineering
Linear algebra
Mechatronics
Optimization
Perturbation theory
Regular Paper
Regularization
Robotics
Uncertainty
제어계측공학
constructive analysis
eigenvalues
fundamental theorem of algebra
Approximate solutions
eigenvectors
ISSN:1598-6446, 2005-4092
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Popis
Shrnutí:The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or Jordan normal forms. Perturbation theory and various regularization techniques help address some numerical difficulties of computation eigenvectors, but often rely on per se uncomputable quantities, such as a minimal gap between eigenvalues. In this note, the eigenvalue problem is revisited within constructive analysis allowing to explicitly consider numerical uncertainty. Exact eigenvectors are substituted by approximate ones in a suitable format. Examples showing influence of computation precision are provided.
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http://link.springer.com/article/10.1007/s12555-018-0571-2
ISSN:1598-6446
2005-4092
DOI:10.1007/s12555-018-0571-2