On the use of Kronecker's algorithm in the generalized rational interpolation problem |
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Authors: | Florent Cordellier |
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Institution: | (1) Laboratoire d'Analyse Numérique et Optimisation, Université des Sciences et Techniques de Lille Flandres-Artois, 59655 Villeneuve d'Ascq Cédex, France |
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Abstract: | Kronecker's algorithm can be used to solve the generalized rational interpolation problem. In order to present the algorithm, rational forms are used here instead of too restrictive rational fractions. The proposed algorithm is reliable as soon as the functionals that characterize the problem satisfy two precise conditions. These conditions are fulfilled in the modified Hermite rational interpolation problem and, as a consequence, in the special case of the Cauchy problem and of the Padé approximation problem. This reliability covers two properties: on one hand, every rational form resulting from the algorithm is a solution of the problem whereas, on the other hand, every solution of the problem is found by the algorithm (with the exception of a possible reduction of the rational form). However, if the algorithm yields a non-reduced rational form, then the corresponding rational fraction is not a solution of the problem. |
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Keywords: | AMS (MOS) 41A21 65D05 |
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