On the denominator values and barycentric weights of rational interpolants
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2007-03-15
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Elsevier B.V.
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We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341-348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355-370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole. (c) 2006 Elsevier B.V. All rights reserved.
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Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 200, n. 2, p. 576-590, 2007.