Interpolation Processes Basic Theory and Applications
The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs, recent results on convergent
- PDF / 5,238,165 Bytes
- 452 Pages / 439.37 x 666.142 pts Page_size
- 51 Downloads / 186 Views
Giuseppe Mastroianni • Gradimir V. Milovanovi´c
Interpolation Processes Basic Theory and Applications
Giuseppe Mastroianni Università della Basilicata Dipartimento di Matematica Via dell’Ateneo Lucano 85100 Potenza, Italy [email protected]
Gradimir V. Milovanovi´c Megatrend University Faculty of Computer Sciences Bulevar umetnosti 29 11070 Novi Beograd, Serbia [email protected]
ISBN 978-3-540-68346-9
e-ISBN 978-3-540-68349-0
DOI 10.1007/978-3-540-68349-0 Springer Monographs in Mathematics ISSN 1439-7382 Library of Congress Control Number: 2008930793 Mathematics Subject Classification (2000): 33-xx, 41-xx, 42Axx, 45A05, 45B05, 45H05, 65B10, 65Dxx © 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
To Ida and Dobrila
Preface
Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that appeared in the last fifty 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 Scientific. 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., results on divergent interpolation processes, usually constructed over some equidistant system of nodes. The present book deals mainly with new results on convergent interpolation 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 field (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 first chapter provides an account of basic facts on approximation by algebraic and trigonometric polynomials i
Data Loading...
