Remarks on interpolation in certain linear spaces (III)

Authors

  • Adrian Diaconu “Babes-Bolyai” University, Cluj-Napoca, Romania

Keywords:

abstract interpolation polynomial, nonlinear mappings between normed spaces

Abstract

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.

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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

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Published

2006-02-01

How to Cite

Diaconu, A. (2006). Remarks on interpolation in certain linear spaces (III). Rev. Anal. Numér. Théor. Approx., 35(1), 41–51. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no1-art6

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