ORTHO research project

Sponsored by

FWO project G.0278.97

Short description

Context :

The aim of this research is to extend the theory of orthogonal systems, to design applications for these generalizations and to find efficient and stable ways to compute the orthogonal systems as well as to solve the applications. The results are translated into the related domains of rational approximation, linear algebra, linear systems and signal processing.

The objectives can be summarized as follows

• Generalizing the theory and the algorithms concerning orthogonal polynomials in more than one variable resulting in fast methods to solve related structured linear systems.
• Based on the fast algorithms to compute vector or matrix orthogonal polynomials, solving structured matrices, e.g., Cauchy and Loewner, in a fast and stable way. Smoothing of signals with several components. Estimating the frequencies and the spectral density of stationary time series.
• Generalizing the theory of orthogonal rational functions to the matrix positive definite case. Developing the theory of formal orthogonal rational functions for the scalar and later for the matrix case.
• Investigating the possibility of replacing orthogonal wavelets by formal orthogonal ones.
• Translating the new results into the related domains.

Researchers

• A. Bultheel
• M. Van Barel

In collaboration with

• Dept. Mathematics and Informatics, Univ. Antwerp (Research group Computer Arithmetic and Numerical Techniques) (A. Cuyt, B. Verdonk)
• Dept. Mathematics, K.U.Leuven (Research group of applied mathematics) (W. Van Assche)

Related research

• Orthogonal rational functions