EXPLICIT MULTIDIMENSIONAL INTERPOLATION AND ITS ERROR
Abstract
The article discusses explicit formulas for multidimensional chaotic interpolation: generalized interpolation formulas of the Newton and Lagrange types. These formulas are generally irrational, but among them, there are polynomial formulas of even order. Estimates of the remainder terms of the generalized Newton and Lagrange interpolation formulas are obtained, as well as for arbitrary interpolation formulas, based solely on the smoothness of the interpolated function and the vanishing of the remainder at the grid points.
Downloads
References
Schumaker L.L. Fitting surfaces to scattered data. - In Approximation theory II. Acad. Press, New York- London, 1976.p.203-268.
Barnxill R.E. Representation and approximation of surfaces. - In mathematical software III. Acad. Press, New York- London,1977. p. 69-120.
Shepard D. A two dimensional interpolation function for irregularly spaced data. –In Proc. 23 rd. Nat. Conf. ASM, 1968. P. 517-524.
Franke R. Locally determined smooth interpolation at irregularly spaced points in several variables. - J. Inst. Math. Appliques, 1977. V.19, p. 471-482.
Duchon J. Interpolation des fonctions de duex variables suivant le principe de la flexion des plaques minces.- R.A.I.R.O.,v.10,
Имомов А. Оценки явных формул многомерной интерполяции в зависимости от класса функций. Молодой учёный. №20 (100) октябрь-2, 2015.
Тыртышников Е.Е. Методы численного анализа. М.: МГУ, 2006.-290 с.
Зорич В.А. Математический анализ.т.2.М.: Наука, 1984.-544 с.
