On the interpolation in linear normed spaces using multiple nodes

Authors

  • Adrian Diaconu "Babeş-Bolyai" University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat441-1060

Keywords:

interpolation in linear normed spaces, multiple nodes
Abstract views: 268

Abstract

In the papers [2], [3], [4], [6], [7] we indicated a method of extending the notion of interpolation polynomial for the case of a non-linear mapping \(f : X \to Y\) where \(X\) and \(Y\) are linear spaces with special structures. This extension o¤ers the possibility to establish, in this general and abstract case as well, the main properties known in the case of the interpolation of real fonctions. To switch to the case using multiple nodes, case that compulsorily uses the notion of Fréchet differential of the ?rst order as well as of superiour orders, we will point out the de?nition and certain properties of these differentials. On this basis we can present the manner of building an abstract interpolation polynomial with multiple nodes.

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References

I. K. Argyros, Polynomial Operator Equation in Abstract Spaces and Applications, CRC Press Boca Raton Boston London New York Washington D.C., (1998).

A. Diaconu, Interpolation dans les espaces abstraits. Méthodes iteratives pour la resolution des equation operationnelles obtenues par l’interpolation inverse (I), Babes-Bolyai University, Faculty of Mathematics, Research Seminars, Preprint No. 4, 1981, Seminar of Functional Analysis and Numerical Methods, pp. 1–52.

A. Diaconu, Interpolation dans les espaces abstraits. Méthodes itératives pour la resolution des équation opérationnelles obtenues par l’interpolation inverse (II), Babes-Bolyai University, Faculty of Mathematics, Research Seminars, Preprint No. 1, 1984, Seminar of Functional Analysis and Numerical Methods, pp. 41–97.

A. Diaconu, Interpolation dans les espaces abstraits. Méthodes itératives pour la resolution des équation opérationnel les obtenues par l’interpolation inverse (III), Babes-Bolyai University, Faculty of Mathematics, Research Seminars, Preprint No. 1, 1985, Seminar of Functional Analysis and Numerical Methods, pp. 21–71.

A. Diaconu, Sur quelques propriétés des dérivées de type Fréchet d’ordre supérieur, Babes-Bolyai University, Faculty of Mathematics, Research Seminaries, Seminar of Functional Analysis and Numerical Methods, Preprint No. 1, (1983), pp. 13–26.

A. Diaconu, Remarks on Interpolation in Certain Linear Spaces (I), Studii in metode de analiza numerica si optimizare, Chisinau: USM-UCCM., 2, 2(1), (2000), pp. 3–14.

A. Diaconu, Remarks on Interpolation in Certain Linear Spaces (II), Studii in metode de analiza numerica si optimizare, Chisinau: USM-UCCM., 2, 2 (4), (2000), pp. 143–161.

V. L. Makarov and V. V. Hlobistov Osnov teorii polinomialnogo operatornogo interpolirovania, Institut Mathematiki H.A.H. Ukrain, Kiev, (1998) ( in Russian).

I. Pavaloiu, Interpolation dans des espaces lineaires normés et application, Mathematica, Cluj, 12(35), 1, (1970), pp. 149–158.

I. Pavaloiu, Consideratii asupra metodelor iterative obtinute prin interpolare inversa, Studii si cercetari matematice, 23, 10, (1971), pp. 1545–1549 (in Romanian).

I. Pavaloiu, Introducere in teoria aproximarii solutiilor ecuatiilor, Editura Dacia, Cluj-Napoca, (1976), (in Romanian).

P. M. Prenter, Lagrange and Hermite interpolation in Banach spaces, J. Approx. Theory, 4 (1971), pp. 419–432, http://doi.org/10.1016/0021-9045(71)90007-4 DOI: https://doi.org/10.1016/0021-9045(71)90007-4

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Published

2015-12-18

How to Cite

Diaconu, A. (2015). On the interpolation in linear normed spaces using multiple nodes. J. Numer. Anal. Approx. Theory, 44(1), 42–61. https://doi.org/10.33993/jnaat441-1060

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