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Introduction to Approximation Theory

Elliot W. Cheney
Publisher: 
AMS
Publication Date: 
2000
Number of Pages: 
259
Format: 
Hardcover
Edition: 
2
Series: 
AMS Chelsea Publishing
Price: 
30.00
ISBN: 
0821813749
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

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Introduction

* 1 Examples and prospectus
* 2 Metric spaces
* 3 Normed linear spaces
* 4 Inner-product spaces
* 5 Convexity
* 6 Existence and unicity of best approximations
* 7 Convex functions

The Tchebycheff Solution of Inconsistent Linear Equations

* 1 Introduction
* 2 Systems of equations with one unknown
* 3 Characterization of the solution
* 4 The special case
* 5 P¢lya's algorithm
* 6 The ascent algorithm
* 7 The descent algorithm
* 8 Convex programming

Tchebycheff Approximation by Polynomials and Other Linear Families

* 1 Introduction
* 2 Interpolation
* 3 The Weierstrass theorem
* 4 General linear families
* 5 the unicity problem
* 6 Discretization errors: General theory
* 7 Discretization: Algebraic polynomials. The inequalities of Markoff and Bernstein
* 8 Algorithms

Least-squares Approximation and Related Topics

* 1 Introduction
* 2 Orthogonal systems of polynomials
* 3 Convergence of orthogonal expansions
* 4 Approximation by series of Tchebycheff polynomials
* 5 Discrete least-squares approximation
* 6 The Jackson theorems

Rational Approximation

* 1 Introduction
* 2 Existence of best rational approximations
* 3 The characterization of best approximations
* 4 Unicity; Continuity of best-approximation operators
* 5 Algorithms
* 6 Pad‚ Approximation and its generalizations
* 7 Continued fractions

Some Additional Topics

* 1 The Stone approximation theorem
* 2 The Mntz theorem
* 3 The converses of the Jackson theorems
* 4 Polygonal approximation and bases in $C[a, b]$
* 5 The Kharshiladze-Lozinski theorems
* 6 Approximation in the mean
* Notes
* References
* Index

Dummy View - NOT TO BE DELETED