Full Hermite Interpolation and Approximation in Topological Fields

Leonard Dăuş, Ghiocel Groza and Marilena Jianu
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Leonard Dăuş: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 020396 Bucharest, Romania
Ghiocel Groza: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 020396 Bucharest, Romania
Marilena Jianu: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 020396 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 11, 1-17

Abstract: By using generalized divided differences, we study the simultaneous interpolation of an m times continuously differentiable function and its derivatives up to a fixed order in a topological field K . If K is a valued field, then simultaneous Hermite interpolation and approximation are considered. Newton interpolating series are used in the case of an infinite number of conditions of interpolation. Applications to the numerical approximation of variational problems, the solution of a functional equation and, in the case of p -adic fields, the representation of solutions of a boundary value problem for an equation of the Fuchsian type illustrate the efficiency of the theoretical results.

Keywords: polynomial approximation; interpolation; generalized divided differences; variational problems; p -adic numbers; functional equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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