Rational interpolation via orthogonal polynomials

AbstractRelations between rational interpolants and Hankel matrices are investigated. A modification of a Jacobi-like algorithm for rational interpolation proposed in [1] is developed. The proposed algorithm eliminates all the auxiliary assumptions required to implement the algorithm of [1]. In this way, it can be used to construct all existing rational interpolants with the cost of O(N2) arithmetic operations where N + 1 is the number of data points