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.