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Orthogonal rational functions and diagonal-plus-semiseparable matrices

The space of all proper rational functions with prescribed real poles is considered. Given a set of points zi on the real line and the weights wi, 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.