Chebyshev polynomials

"Chebyshev polynomials are encountered in virtually every area of numerical analysis, and they hold particular importance 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 equation. Problems in each chapter, ranging in difficulty from elementary to quite advanced, reinforce the concepts and methods presented."--Jacket

DEFINITIONS; Preliminary Remarks; Trigonometric Definitions and Recurrences; Shifted Chebyshev Polynomials; Chebyshev Polynomials of a Complex Variable; BASIC PROPERTIES AND FORMULAE; Introduction; Chebyshev Polynomial Zeros and Extrema; Chebyshev Polynomials and Power of x; Evaluation of Chebyshev Sums, Products,

Integrals and Derivatives; MINIMAX PROPERTIES AND ITS APPLICATIONS; Approximation-Theory and Structure; Best and Minimax Approximation; The Minimax Property of the Chebyshev Polynomials; The Chebyshev Semi-Iterative Method for Linear Equations; Telescoping Procedures for Power Series; The Tau Method for Series and Rational Functions; ORTHOGONALITY AND LEAST-SQUARES APPROXIMATION; Introduction-From Minimax to Least Squares; Orthogonality of Chebyshev Polynomials; Orthogonal Polynomials and Best L2 Approximations; Recurrence Relations; Rodriques' Formulae and Differential Equations; Discrete Orthogonality of Chebyshev Polynomials; Discrete Chebyshev Transforms and the FFT; Discrete Data Fitting by Orthogonal Polynomials-The Forsythe-Clenshaw Methods; Orthogonality in the Complex Plane; CHEBYSHEV SERIES; Introduction-Chebyshev Series and Other Expansions; Some Explicit Che…