Orthogonal rational functions and diagonal-plus-semiseparable matrices

Marc Van Barel; Dario Fasino; Luca Gemignani; Nicola Mastronardi

doi:10.1117/12.453815

6 December 2002 Orthogonal rational functions and diagonal-plus-semiseparable matrices

Marc Van Barel, Dario Fasino, Luca Gemignani, Nicola Mastronardi

Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII; (2002) https://doi.org/10.1117/12.453815
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

The space of all proper rational functions with prescribed real poles is considered. Given a set of points z_i on the real line and the weights w_i, we define the discrete inner product (formula in paper). In this paper we derive an efficient method to compute the coefficients of a recurrence relation generating a set of orthonormal rational basis functions with respect to the discrete inner product. We will show that these coefficients can be computed by solving an inverse eigenvalue problem for a diagonal-plus-semiseparable matrix.

Citation Download Citation

Marc Van Barel, Dario Fasino, Luca Gemignani, and Nicola Mastronardi "Orthogonal rational functions and diagonal-plus-semiseparable matrices", Proc. SPIE 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII, (6 December 2002); https://doi.org/10.1117/12.453815

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