Interpolation Processes - Basic Theory and Applications (Hardcover, 2008 ed.)

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. Vertesi: 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 this eld (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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Springer Monographs in Mathematics
Release date:	September 2008
First published:	2009
Authors:	Giuseppe Mastroianni • Gradimir Milovanovic
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Hardcover
Pages:	446
Edition:	2008 ed.
ISBN-13:	978-3-540-68346-9
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
LSN:	3-540-68346-1
Barcode:	9783540683469

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