Interpolation and Approximation by Polynomials

By: George M. Phillips

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Hardcover | 8 April 2003

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332 Pages

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23.5 x 15.24 x 1.91

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This book covers the main topics concerned with interpolation and approximation by polynomials. This subject can be traced back to the precalculus era but has enjoyed most of its growth and development since the end of the nineteenth century and is still a lively and flourishing part of mathematics. In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. George Phillips has lectured and researched in mathematics at the University of St. Andrews, Scotland. His most recent book, Two Millenia of Mathematics: From Archimedes to Gauss (Springer 2000), received enthusiastic reviews in the USA, Britain and Canada. He is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Industry Reviews

From the reviews:

G.M. Phillips

Interpolation and Approximation by Polynomials

"A very nicely written textbook to learn about polynomial interpolation and approximation."

-ZENTRALBLATT MATH

"This book contains selected topics from approximation theory. The author discusses one of 'the most' classic part of approximation theory, the interpolation theory and two related fields ... . The selection of the areas, the lot of worked examples, the exercises and problems at the end of each section and the algorithms included and detailed ... makes this book perfect for everyone's approximation book." (Bela Nagy, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

"This is a very nicely written textbook to learn about polynomial interpolation and approximation. ... Throughout the book nice sets of 'Problems' are placed ... ." (Marcel G. de Bruin, Zentralblatt MATH, Vol. 1023, 2003)

"This monograph may be considered as the successor of P. Davis' Interpolation and Approximation (1963) ... . it is an excellent introduction to the topic. ... This book is well suited for a course on numerical analysis and approximation theory with emphasis on the topic mentioned in the title. ... even more a course book because each section ends with a list of exercises, and the text contains many explicit examples." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, 2007)

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Preface	p. vii
Univariate Interpolation	p. 1
Introduction	p. 1
The Vandermonde Equations	p. 16
Forward Differences	p. 28
Central Differences	p. 40
q-Differences	p. 43
Best Approximation	p. 49
The Legendre Polynomials	p. 49
The Chebyshev Polynomials	p. 64
Finite Point Sets	p. 82
Minimax Approximation	p. 87
The Lebesgue Function	p. 100
The Modulus of Continuity	p. 116
Numerical Integration	p. 119
Interpolatory Rules	p. 119
The Euler-Maclaurin Formula	p. 133
Gaussian Rules	p. 143
Peano's Theorem and Applications	p. 147
Peano Kernels	p. 147
Further Properties	p. 153
Multivariate Interpolation	p. 163
Rectangular Regions	p. 163
Triangular Regions	p. 176
Integration on the Triangle	p. 188
Interpolation on the q-Integers	p. 195
Splines	p. 215
Introduction	p. 215
B-Splines	p. 218
Equally Spaced Knots	p. 229
Knots at the q-Integers	p. 239
Bernstein Polynomials	p. 247
Introduction	p. 247
The Monotone Operator Theorem	p. 263
On the q-Integers	p. 267
Total Positivity	p. 274
Further Results	p. 280
Properties of the q-Integers	p. 291
The q-Integers	p. 291
Gaussian Polynomials	p. 296
References	p. 305
Index	p. 309
Table of Contents provided by Ingram. All Rights Reserved.

Interpolation and Approximation by Polynomials

At a Glance

Hardcover

Industry Reviews

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