Skip to main content

Interpolation Processes

Basic Theory and Applications

  • Book
  • © 2008

Overview

  • 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 as is this book
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Monographs in Mathematics (SMM)

This is a preview of subscription content, log in via an institution to check access.

Access this book

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (5 chapters)

Keywords

About this book

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.

Reviews

From the reviews:

"The entire book deals almost exclusively with the interpolation of univariate functions … . I believe that this book has the potential to become a standard reference work in this area. It will certainly be very useful to anyone conducting research in this field, both as a beginner and as an advanced scientist. In addition, it provides a large amount of helpful information to people from other fields, who need to use interpolation methods in their daily work." (Kai Diethelm, ACM Computing Reviews, May, 2009)

"A distinctive feature of the present book is the emphasis on convergent interpolation processes in uniform norm, for algebraic and trigonometric polynomials. … The authors have made substantial contributions to the subject, and the book deals mainly with new results, not yet published in other textbooks and monographs. Intended for researchers and students in mathematics, physics, and applied sciences, the book will be welcomed by allspecialists in these areas." (Ioan Rasa, Zentralblatt MATH, Vol. 1154, 2009)

"It contains mostly theoretical results in a wide area of approximation theory, but in many places numerical applications are also given. … This is a well-written book containing the most up-to-date information on the subjects covered. It can be useful for both experts in the field as well as those who have a basic knowledge in mathematical analysis. A list of more than 500 publications is provided, and an eight-page index makes the search for topics easier." (J. Szabados, Mathematical Reviews, Issue 2009 i)

Authors and Affiliations

  • Dipartimento di Matematica, Università della Basilicata, Potenza, Italy

    Giuseppe Mastroianni

  • Faculty of Computer Sciences, Megatrend University, Novi Beograd, Serbia

    Gradimir V. Milovanović

About the authors

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

Bibliographic Information

Publish with us