Numerical operations among rational matrices: standard techniques and interpolation
Petr Hušek; Michael Šebek; Jan Štecha
Kybernetika (1999)
- Volume: 35, Issue: 5, page [587]-598
- ISSN: 0023-5954
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topHušek, Petr, Šebek, Michael, and Štecha, Jan. "Numerical operations among rational matrices: standard techniques and interpolation." Kybernetika 35.5 (1999): [587]-598. <http://eudml.org/doc/33447>.
@article{Hušek1999,
abstract = {Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matrices corresponding to each particular point. Finally, the resulting rational matrix is recovered from the particular constant solutions via interpolation. It may be computed either in polynomial matrix fraction form or as matrix of rational functions. The operations considered include addition, multiplication and computation of polynomial matrix fraction form. The standard and interpolation methods are compared by experiments.},
author = {Hušek, Petr, Šebek, Michael, Štecha, Jan},
journal = {Kybernetika},
keywords = {rational matrix; interpolation method; polynomial matrix fraction form; numerically attractive alternative; rational matrix; interpolation method; polynomial matrix fraction form; numerically attractive alternative},
language = {eng},
number = {5},
pages = {[587]-598},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Numerical operations among rational matrices: standard techniques and interpolation},
url = {http://eudml.org/doc/33447},
volume = {35},
year = {1999},
}
TY - JOUR
AU - Hušek, Petr
AU - Šebek, Michael
AU - Štecha, Jan
TI - Numerical operations among rational matrices: standard techniques and interpolation
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 5
SP - [587]
EP - 598
AB - Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matrices corresponding to each particular point. Finally, the resulting rational matrix is recovered from the particular constant solutions via interpolation. It may be computed either in polynomial matrix fraction form or as matrix of rational functions. The operations considered include addition, multiplication and computation of polynomial matrix fraction form. The standard and interpolation methods are compared by experiments.
LA - eng
KW - rational matrix; interpolation method; polynomial matrix fraction form; numerically attractive alternative; rational matrix; interpolation method; polynomial matrix fraction form; numerically attractive alternative
UR - http://eudml.org/doc/33447
ER -
References
top- Antsaklis P. J., Gao Z., 10.1080/00207179308923007, Internat. J. Control 58 (1993), 2, 349–404 (1993) Zbl0776.41001MR1229855DOI10.1080/00207179308923007
- Šebek M., Strijbos R. C., Polynomial control toolbox, In: Proceedings of the 4th IEEE Mediterranean Symposium on New Directions in Control & Automation, IEEE–CSS, Chania 1996, pp. 488–491 (1996)
- Kučera V., Discrete Linear Control: The Polynomial Equation Approach, Academia, Praha 1979 Zbl0432.93001MR0573447
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