Geodesic
Numerical operations among rational matrices: standard techniques and interpolation
Kybernetika, Tome 35 (1999) no. 5, pp. 587-598 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 65F30, 93B25, 93B40
Keywords: rational matrix; interpolation method; polynomial matrix fraction form; numerically attractive alternative 
@article{KYB_1999_35_5_a2,
     author = {Hu\v{s}ek, Petr and \v{S}ebek, Michael and \v{S}techa, Jan},
     title = {Numerical operations among rational matrices: standard techniques and interpolation},
     journal = {Kybernetika},
     pages = {587--598},
     year = {1999},
     volume = {35},
     number = {5},
     mrnumber = {1728469},
     zbl = {1274.93063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_5_a2/}
}
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
SP  - 587
EP  - 598
VL  - 35
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/KYB_1999_35_5_a2/
LA  - en
ID  - KYB_1999_35_5_a2
ER  - 
%0 Journal Article
%A Hušek, Petr
%A Šebek, Michael
%A Štecha, Jan
%T Numerical operations among rational matrices: standard techniques and interpolation
%J Kybernetika
%D 1999
%P 587-598
%V 35
%N 5
%U http://geodesic.mathdoc.fr/item/KYB_1999_35_5_a2/
%G en
%F KYB_1999_35_5_a2
Hušek, Petr; Šebek, Michael; Štecha, Jan. Numerical operations among rational matrices: standard techniques and interpolation. Kybernetika, Tome 35 (1999) no. 5, pp. 587-598. http://geodesic.mathdoc.fr/item/KYB_1999_35_5_a2/

[1] Antsaklis P. J., Gao Z.: Polynomial and Rational Matrix Interpolation: Theory and Control Applications. Internat. J. Control 58 (1993), 2, 349–404 | DOI | MR | Zbl

[2] 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

[3] Kučera V.: Discrete Linear Control: The Polynomial Equation Approach. Academia, Praha 1979 | MR | Zbl