Interpolation Processes
Description
Reviews / Votes
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)
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Persons
Gradimir V. Milovanovic is Professor of the University of Nis and Corresponding member of the Serbian Academy of Sciences and Arts.
Content
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.