Orthogonality Measures and Applications in Systems Theory in One and More Variables

Authors:
Adhemar Bultheel;Annie Cuyt;Brigitte Verdonk
Affiliations:
Dept of Computer Science, Katholieke Universiteit Leuven, Heverlee, Belgium B3001;Dept of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium B2020;Dept of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium B2020
Venue:
Large-Scale Scientific Computing
Year:
2009

Citing 4
Cited 0

Pade´ techniques for model reduction in linear system theory: a survey

Journal of Computational and Applied Mathematics
Properties of multivariate homogeneous orthogonal polynomials

Journal of Approximation Theory
Multidimensional Digital Signal Processing

Multidimensional Digital Signal Processing
Stable multi-dimensional model reduction and IIR filter design

International Journal of Computing Science and Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The representation or order reduction of a rational transfer function by a linear combination of orthogonal rational functions offers several advantages, among which the possibility to work with prescribed poles and hence the guarantee of system stability. Also for multidimensional linear shift-invariant systems with infinite-extent impulse response, stability can be guaranteed a priori by the use of a multivariate Padé-type approximation technique, which is again a rational approximation technique. In both the one- and multidimensional case the choice of the moment functional with respect to which the orthogonality of the functions in use is imposed, plays a crucial role.