Interpolation Processes: Basic Theory and Applications - Couverture souple

Livre 52 sur 184: Springer Monographs in Mathematics

Mastroianni, Giuseppe; Milovanovic, Gradimir

 
9783642087943: Interpolation Processes: Basic Theory and Applications

Synopsis

Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses,usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in thiseld (orthogonal polynomials, moduli of smoothness,K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.

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À propos de l?auteur

Gradimir V. Milovanovic is Professor of the University of Nis and Corresponding member of the Serbian Academy of Sciences and Arts.

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Autres éditions populaires du même titre

9783540683469: Interpolation Processes: Basic Theory and Applications

Edition présentée

ISBN 10 :  3540683461 ISBN 13 :  9783540683469
Editeur : Springer-Verlag Berlin and Heide..., 2008
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