Chebyshev polynomials. (©2003)

• Record Type: Book
• Further Information: Note: John C. Mason, David Handscomb.
• Other Names: Mason, J. C; Handscomb, D. C (David Christopher)
• Contents: 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 Chebyshev Series Expansions; Fourier-Chebyshev Series and Fourier Theory; Projections and Near-Best Approximations; Near-Minimax Approximation by a Chebyshev Series; Comparison of Chebyshev and Other Polynomial Expansions; The Error of a Truncated Chebyshev Expansion; Series of Second-, Third-, and Fourth-Kind Polynomials; Lacunary Chebyshev Series; Chebyshev Series in the Complex Domain; CHEBYSHEV INTERPOLATION; Polynomial Interpolation; Orthogonal Interpolation; Chebyshev Interpolation Formulae; Best L1 Approximation by Chebyshev Interpolation; Near-Minimax Approximation by Chebyshev Interpolation; NEAR-BEST L8, L1, and Lp APPROXIMATIONS; Near-Best L8 (Near-Minimax) Approximations; Near-Best L1 Approximations; Best and Near-Best Lp Approximations; INTEGRATION USING CHEBYSHEV POLYNOMIALS; Indefinite Integration with Chebyshev Series; Gauss-Chebyshev Quadrature; Quadrature Methods of Clenshaw-Curtis Type; Error Estimation for Clenshaw-Curtis Methods; Some other Work on Clenshaw-Curtis Methods; SOLUTION OF INTEGRAL EQUATIONS; Introduction; Fredholm Equations of the Second Kind; Fredholm Equations of the Third Kind; Fredholm Equations of the First Kind; Singular Kernels; Regularisation of Integral Equations; Partial Differential Equations and Boundary Integral Equation Methods; SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS; Introduction; A Simple Example; The Original Lanczos Tau Method; A More General Linear Equation; Pseudospectral Methods-Another Form of Collocation; Nonlinear Equations; Eigenvalue Problems; Differential Equations in One Space and One Time Dimension; CHEBYSHEV AND SPECTRAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS; Introduction; Interior, Boundary, and Mixed Methods; Differentiation Matrices and Nodal Representation; Method of Weighted Residuals; Chebyshev Series and Galerkin Methods; Collocation/Interpolation and Related Methods; PDE Methods; Some PDE Problems and Various Methods; Computational Fluid Dynamics; Particular Issues in Spectral Methods; More Advanced Problems; CONCLUSION; BIBLIOGRAPHY; APPENDICES; Biographical Note; Summary of Notations, Definitions, and Important Properties; Tables of Coefficients; INDEX; ; Each chapter also contains a section of Problems.
• Publisher Details: Boca Raton, Fla : Chapman & Hall/CRC
• Publication Date: 2003
• Copyright Date: 2003
• Extent: 1 online resource (xiii, 341 pages), illustrations
• Subjects: 515/.55; Chebyshev polynomials; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Chebyshev polynomials; Orthogonale reeksen; Polynomen; Electronic books
• Languages: English
• ISBNs: 1420036114; 9781420036114
• Related ISBNs: 0849303559; 9780849303555
• Notes: Note: Includes bibliographical references (pages 305-319) and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.