Abstract
The space of all proper rational functions with prescribed real poles is considered. Given a set of points <i>z</i><i><sub>i</sub></i> on the real line and the weights <i>w<sub>i</sub></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.
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