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.
Table of Contents
Definitions. Basic Properties and Formulae. Minimax Properties and Applications. Orthogonality and Least-Squares Approximation. Chebyshev Series. Chebyshev Interpolation. Near-Best Approximations. Integration using Chebyshev Polynomials. Solution of Integral Equations. Solution of Ordinary Differential Equations. Solution of Partial Differential Equations. Conclusion. Bibliography. Appendices.
"The book presents a wide panorama of the applications of Chebyshev polynomials to scientific computing. [It] is very clearly written and is a pleasure to read. Examples inserted in the text allow one to test his or her ability to understand and use the methods, which are described in detail, and each chapter ends with a section full of very pedagogical problems."
Mathematics of Computation
"The book, by two well known specialists, is well written and presented. Many examples are given and problems have been added for students. It is a book that every numerical analyst should have."
- Numerical Algorithms
"… a modern treatment of the subject … in a carefully prepared way … very well produced … "
- Mathematical Reviews, Issue 2004h