Giuseppe Mastroianni, Gradimir Milovanovic

Interpolation Processes (eBook, PDF)

Basic Theory and Applications

• Format: PDF

Produktbeschreibung

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 interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In this special, but fundamental and important field of real analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. 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. Beside the basic properties of the classical orthogonal polynomials the book provides new resultson nonclassical orthogonal polynomials including methods for their numerical construction.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 446
• Erscheinungstermin: 24. August 2008
• Englisch
• ISBN-13: 9783540683490
• Artikelnr.: 37358954

Autorenporträt

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

Inhaltsangabe

1. Constructive Elements and Approaches in Approximation Theory.- 1.1 Introduction to Approximation Theory.- 1.2 Basic Facts on Trigonometric Approximation.- 1.3 Chebyshev Systems and Interpolation.- 1.4 Interpolation by Algebraic Polynomials.- 2. Orthogonal Polynomials and Weighted Polynomial Approximation.- 2.1 Orthogonal Systems and Polynomials.- 2.2 Orthogonal Polynomials on the Real Line.- 2.3 Classical Orthogonal Polynomials.- 2.4 Nonclassical Orthogonal Polynomials.- 2.5 Weighted Polynomial Approximation.- 3. Trigonometric Approximation.- 3.1 Approximating Properties of Operators.- 3.2 Discrete Operators.- 4. Algebraic Interpolation in Uniform Norm.- 4.1 Introduction and Preliminaries.- 4.2 Optimal Systems of Nodes.- 4.3 Weighted Interpolation.- 5. Applications.- 5.1 Quadrature Formulae.- 5.2 Integral Equations.- 5.3 Moment-Preserving Approximation.- 5.4 Summation of Slowly Convergent Series.- References.- Index.

Rezensionen

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)