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Interpolation processes [electronic resource] : basic theory and applications / Giuseppe Mastroianni, Gradimir V. Milovanović

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Presents with proofs the results on convergent interpolation processes, for trigonometric and algebraic polynomials of one real variable. This book provides the basic properties of the classical orthogonal polynomials and results on nonclassical orthogonal polynomials including methods for their num...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Mastroianni, G. (Giuseppe)
Other Authors: Milovanović, G. V.
Format: Electronic eBook
Language:English
Published: Berlin : Springer, ©2008.
Series:Springer monographs in mathematics.
Subjects:
Interpolation.
Table of Contents:
  • 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.

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