Research Catalog

Title

Chebyshev polynomials / J.C. Mason, D.C. Handscomb.

Author

Mason, J. C.

Publication

Boca Raton, Fla. : Chapman & Hall/CRC, c2003.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Handscomb, D. C. (David Christopher)

Description

xiii, 341 p. : ill.; 25 cm.

Summary

• "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.

Subject

Chebyshev polynomials

Bibliography (note)

• Includes bibliographical references (p. 305-319) and index.

Processing Action (note)

• committed to retain

Contents

Preliminary remarks -- Trigonometric definitions and recurrences -- The first-kind polynomial T[subscript n] -- The second-kind polynomial U[subscript n] -- The third- and fourth-kind polynomials V[subscript n] and W[subscript n] (the airfoil polynomials) -- Connections between the four kinds of polynomial -- Shifted Chebyshev polynomials -- The shifted polynomials T*[subscript n], U*[subscript n], V*[subscript n], W*[subscript n] -- Chebyshev polynomials for the general range [a, b] -- Chebyshev polynomials of a complex variable -- Conformal mapping of a circle to and from an ellipse -- Chebyshev polynomials in z -- Shabat polynomials -- Basic Properties and Formulae -- Chebyshev polynomial zeros and extrema -- Relations between Chebyshev polynomials and powers of x -- Powers of x in terms of {T[subscript n](x)} -- T[subscript n](x) in terms of powers of x -- Ratios of coefficients in T[subscript n](x) -- Evaluation of Chebyshev sums, products, integrals and derivatives -- Evaluation of a Chebyshev sum -- Stability of the evaluation of a Chebyshev sum -- Evaluation of a product -- Evaluation of an integral -- Evaluation of a derivative -- The Minimax Property and Its Applications -- Approximation--theory and structure -- The approximation problem -- Best and minimax approximation -- The minimax property of the Chebyshev polynomials -- Weighted Chebyshev polynomials of second, third and fourth kinds -- The Chebyshev semi-iterative method for linear equations -- Telescoping procedures for power series.

ISBN

0849303559 (alk. paper)

LCCN

^^2002073578

Owning Institutions

Harvard Library