AMS Chelsea Publishing 1982; 259 pp; hardcover Volume: 317 Reprint/Revision History: second AMS printing 2000 ISBN10: 0821813749 ISBN13: 9780821813744 List Price: US$38 Member Price: US$34.20 Order Code: CHEL/317.H
 This volume contains historical background and discussion of results for each chapter, References, and an Index. Reviews From a review of the original edition ... "In this book, which is intended to be an introduction to the subject, the author steers a middle course between the various viewpoints. On the one hand, he presents his material within the framework of (elementary) functional analysis ... and on the other hand he treats various algorithms which prepare the way for the numerical solution of various types of approximation problems. One of the highlights of the book is Chapter V on rational approximation which is an important case of nonlinear approximation ... The book concludes with a detailed and interesting section on historical notes and a lengthy bibliography. There are approximately 430 good exercises. The author has provided a usable and very versatile text which is certainly to be recommended."  Mathematical Reviews "E. W. Cheney's highly respected and wellknown book ... covers an enormous amount of material ... [It] is written with a clarity and precision which those who are familiar with the author's many papers have come to expect ... There is an appendix which supplements each chapter with copious notes and serves to place the particular topic in historical perspective ... [T]he notes are invaluable; their effect is to make a small book almost encyclopedic in character. ... In the quality of its exposition and the skill and craft manifest in its organization, the book is a classic with few competitors. Anyone involved with computer mathematics will want it nearby."  Computing Reviews Table of Contents Introduction  1 Examples and prospectus
 2 Metric spaces
 3 Normed linear spaces
 4 Innerproduct 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 Pólya'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
Leastsquares 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 leastsquares 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 bestapproximation operators
 5 Algorithms
 6 Padé Approximation and its generalizations
 7 Continued fractions
Some Additional Topics  1 The Stone approximation theorem
 2 The Müntz theorem
 3 The converses of the Jackson theorems
 4 Polygonal approximation and bases in \(C[a, b]\)
 5 The KharshiladzeLozinski theorems
 6 Approximation in the mean
 Notes
 References
 Index
