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 interpolation processes, for trigonometric a...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2008, 2008
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| Edition: | 1st ed. 2008 |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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