Remarks on interpolation in certain linear spaces (III)
DOI:
https://doi.org/10.33993/jnaat351-1009Keywords:
abstract interpolation polynomial, nonlinear mappings between normed spacesAbstract
In this paper we study a way of extending the model of interpolating the real functions, with simple nodes, to the case of the functions defined between linear spaces, especially between linear normed spaces. In order to keep as many characteristics as possible from the case of the interpolation of real functions, in this paper we present a model of construction of the abstract interpolation polynomials, based on the properties of multilinear mappings. In this case we will define the divided differences and establish interpolation formulas with the rest expressed as a divided difference. We give the example of the type of interpolation polynomial built for non-linear mappings between spaces of functions defined on a certain interval.Downloads
References
Argyros, I. K., Polynomial Operator Equation in Abstract Spaces and Applications, CRC Press Boca Raton, Boston London New York Washington D.C., 1998.
Diaconu, A., Interpolation dans les espaces abstraits. Méthodes itératives pour la resolution des équation opérationnelles obtenues par l'interpolation inverse (I), "Babeş-Bolyai" University, Faculty of Mathematics, Research Seminars, Seminar of Functional Analysis and Numerical Methods, Preprint no. 4, pp. 1-52, 1981.
Diaconu, A., Interpolation dans les espaces abstraits. Méthodes itératives pour la resolution des équation opérationnelles obtenues par l'interpolation inverse (II), "Babeş-Bolyai" University, Faculty of Mathematics, Research Seminars, Seminar of Functional Analysis and Numerical Methods, Preprint no. 1, pp. 41-97, 1984.
Diaconu, A., Interpolation dans les espaces abstraits. Méthodes itératives pour la resolution des équation opérationnelles obtenues par l'interpolation inverse (III), "Babeş-Bolyai" University, Faculty of Mathematics, Research Seminars, Seminar of Functional Analysis and Numerical Methods, Preprint no. 1, pp. 21-71, 1985.
Diaconu, A., Remarks on Interpolation in Certain Linear Spaces (I), Studii în metode de analiză numerică şi optimizare, Chişinău: USM-UCCM, 2, no. 2(1), pp. 3-14, 2000.
Diaconu, A., Remarks on Interpolation in Certain Linear Spaces (II), Studii în metode de analiză numerică şi optimizare, Chişinău: USM-UCCM, 2, no. 2(4), pp. 143-161, 2000.
Makarov, V. L., Hlobistov, V. V., Osnovî teorii polinomialnogo operatornogo interpolirovania, Institut Mathematiki H.A.H. Ukrain, Kiev, 1998 (in Russian).
Păvăloiu, I., Interpolation dans des espaces linéaire normés et application, Mathematica, Cluj, 12(35), 1, pp. 149-158, 1970.
Păvăloiu, I., Consideraţii asupra metodelor iterative obţinute prin interpolare inversă, Studii şi cercetări matematice, 23, 10, pp. 1545-1549, 1971 (in Romanian).
Păvăloiu, I., Introducere în teoria aproximării soluţiilor ecuaţiilor, Editura Dacia, Cluj-Napoca, 1976 (in Romanian).
Prenter, P., M., Lagrange and Hermite interpolation in Banach spaces, Journal of Approximation Theory 4, pp. 419-432, 1971, https://doi.org/10.1016/0021-9045(71)90007-4 DOI: https://doi.org/10.1016/0021-9045(71)90007-4
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
