Chebyshev Polynomials

J.C. Mason, D.C. Handscomb

354 pages, parution le 28/11/2002

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Résumé

Chebyshev polynomials crop up in virtually every area of numerical analysis, and they hold particular importance in recent advances in subjects such as orthogonal polynomials, polynomial approximation, numerical integration, and spectral methods. Yet no book dedicated to Chebyshev polynomials has been published since 1990, and even that work focused primarily on the theoretical aspects. A broad, up-to-date treatment is long overdue.

Providing highly readable exposition on the subject's state of the art, Chebyshev Polynomials is just such a treatment. It includes rigorous yet down-to-earth coverage of the theory along with an in-depth look at the properties of all four kinds of Chebyshev polynomials-properties that lead to a range of results in areas such as approximation, series expansions, interpolation, quadrature, and integral equations. Problems in each chapter, ranging in difficulty from elementary to quite advanced, reinforce the concepts and methods presented.

Far from being an esoteric subject, Chebyshev polynomials lead one on a journey through all areas of numerical analysis. This book is the ideal vehicle with which to begin this journey and one that will also serve as a standard reference for many years to come.

Provides the first up-to-date, practical treatment of Chebyshev polynomials
Discusses theoretical aspects, including definitions, properties, and key formulae for generating the polynomials and computing the expressions that involve them
Includes practical discussions centering on applications such as polynomial approximation, rational approximation, integration, integral equations, and ordinary and partial differential equations, particularly the tau and spectral methods
Includes problem sets in each chapter

Contents

Definitions
Basic Properties and Formulae
The Minimax Property and Its Applications
Orthogonality and Least-Squares Approximation
Chebyshev Series
Chebyshev Interpolation
Near-Best L&#8734, L1, and Lp Approximations
Integration Using Chebyshev Polynomials
Solution of Integral Equations
Solution of Ordinary Differential Equations
Chebyshev and Spectral Methods for partial Differential Equations

L'auteur - J.C. Mason

University of Huddersfield, Queensgate, England

L'auteur - D.C. Handscomb

Oxford University Computing Laboratory, England

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	J.C. Mason, D.C. Handscomb
Parution	28/11/2002
Nb. de pages	354
Format	16 x 24
Couverture	Relié
Poids	634g
Intérieur	Noir et Blanc
EAN13	9780849303555
ISBN13	978-0-8493-0355-5