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TW 350
M. Van Barel, D. Fasino, L. Gemignani, N. Mastronardi
Orthogonal Rational Functions and Structured Matrices
Abstract
The space of all proper rational functions with prescribed poles is considered. Given a set of points zi in the complex plane and the weights wi, we define the discrete inner product
< φ,ψ > := ∑i=0n |wi|2 \overline{φ(zi)} ψ(zi).
In this paper we derive a 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 matrix having a specific structure. In case where all the points zi lie on the real line or on the unit circle, the computational complexity is reduced by an order of magnitude. report.pdf / mailto: M. Van Barel