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図書

図書
J.C. Mason, D.C. Handscomb
出版情報: Boca Raton, Florida : Chapman & Hall/CRC, c2003  xiii, 341 p. ; 25 cm
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目次情報: 続きを見る
Definitions / 1:
Preliminary remarks / 1.1:
Trigonometric definitions and recurrences / 1.2:
The first-kind polynomial T[subscript n] / 1.2.1:
The second-kind polynomial U[subscript n] / 1.2.2:
The third- and fourth-kind polynomials V[subscript n] and W[subscript n] (the airfoil polynomials) / 1.2.3:
Connections between the four kinds of polynomial / 1.2.4:
Shifted Chebyshev polynomials / 1.3:
The shifted polynomials T*[subscript n], U*[subscript n], V*[subscript n], W*[subscript n] / 1.3.1:
Chebyshev polynomials for the general range [a, b] / 1.3.2:
Chebyshev polynomials of a complex variable / 1.4:
Conformal mapping of a circle to and from an ellipse / 1.4.1:
Chebyshev polynomials in z / 1.4.2:
Shabat polynomials / 1.4.3:
Problems for Chapter 1 / 1.5:
Basic Properties and Formulae / 2:
Introduction / 2.1:
Chebyshev polynomial zeros and extrema / 2.2:
Relations between Chebyshev polynomials and powers of x / 2.3:
Powers of x in terms of {T[subscript n](x)} / 2.3.1:
T[subscript n](x) in terms of powers of x / 2.3.2:
Ratios of coefficients in T[subscript n](x) / 2.3.3:
Evaluation of Chebyshev sums, products, integrals and derivatives / 2.4:
Evaluation of a Chebyshev sum / 2.4.1:
Stability of the evaluation of a Chebyshev sum / 2.4.2:
Evaluation of a product / 2.4.3:
Evaluation of an integral / 2.4.4:
Evaluation of a derivative / 2.4.5:
Problems for Chapter 2 / 2.5:
The Minimax Property and Its Applications / 3:
Approximation--theory and structure / 3.1:
The approximation problem / 3.1.1:
Best and minimax approximation / 3.2:
The minimax property of the Chebyshev polynomials / 3.3:
Weighted Chebyshev polynomials of second, third and fourth kinds / 3.3.1:
The Chebyshev semi-iterative method for linear equations / 3.4:
Telescoping procedures for power series / 3.5:
Shifted Chebyshev polynomials on [0, 1] / 3.5.1:
Implementation of efficient algorithms / 3.5.2:
The tau method for series and rational functions / 3.6:
The extended tau method / 3.6.1:
Problems for Chapter 3 / 3.7:
Orthogonality and Least-Squares Approximation / 4:
Introduction--from minimax to least squares / 4.1:
Orthogonality of Chebyshev polynomials / 4.2:
Orthogonal polynomials and weight functions / 4.2.1:
Chebyshev polynomials as orthogonal polynomials / 4.2.2:
Orthogonal polynomials and best L[subscript 2] approximations / 4.3:
Orthogonal polynomial expansions / 4.3.1:
Convergence in L[subscript 2] of orthogonal expansions / 4.3.2:
Recurrence relations / 4.4:
Rodrigues' formulae and differential equations / 4.5:
Discrete orthogonality of Chebyshev polynomials / 4.6:
First-kind polynomials / 4.6.1:
Second-kind polynomials / 4.6.2:
Third- and fourth-kind polynomials / 4.6.3:
Discrete Chebyshev transforms and the fast Fourier transform / 4.7:
The fast Fourier transform / 4.7.1:
Discrete data fitting by orthogonal polynomials: the Forsythe-Clenshaw method / 4.8:
Bivariate discrete data fitting on or near a family of lines or curves / 4.8.1:
Orthogonality in the complex plane / 4.9:
Problems for Chapter 4 / 4.10:
Chebyshev Series / 5:
Introduction--Chebyshev series and other expansions / 5.1:
Some explicit Chebyshev series expansions / 5.2:
Generating functions / 5.2.1:
Approximate series expansions / 5.2.2:
Fourier-Chebyshev series and Fourier theory / 5.3:
L[subscript 2]-convergence / 5.3.1:
Pointwise and uniform convergence / 5.3.2:
Bivariate and multivariate Chebyshev series expansions / 5.3.3:
Projections and near-best approximations / 5.4:
Near-minimax approximation by a Chebyshev series / 5.5:
Equality of the norm to [lambda][subscript n] / 5.5.1:
Comparison of Chebyshev and other orthogonal polynomial expansions / 5.6:
The error of a truncated Chebyshev expansion / 5.7:
Series of second-, third- and fourth-kind polynomials / 5.8:
Series of second-kind polynomials / 5.8.1:
Series of third-kind polynomials / 5.8.2:
Multivariate Chebyshev series / 5.8.3:
Lacunary Chebyshev series / 5.9:
Chebyshev series in the complex domain / 5.10:
Chebyshev-Pade approximations / 5.10.1:
Problems for Chapter 5 / 5.11:
Chebyshev Interpolation / 6:
Polynomial interpolation / 6.1:
Orthogonal interpolation / 6.2:
Chebyshev interpolation formulae / 6.3:
Aliasing / 6.3.1:
Second-kind interpolation / 6.3.2:
Third- and fourth-kind interpolation / 6.3.3:
Conditioning / 6.3.4:
Best L[subscript 1] approximation by Chebyshev interpolation / 6.4:
Near-minimax approximation by Chebyshev interpolation / 6.5:
Problems for Chapter 6 / 6.6:
Near-Best L[subscript [infinity]], L[subscript 1] and L[subscript p] Approximations / 7:
Near-best L[subscript [infinity]] (near-minimax) approximations / 7.1:
Second-kind expansions in L[subscript [infinity]] / 7.1.1:
Third-kind expansions in L[subscript [infinity]] / 7.1.2:
Near-best L[subscript 1] approximations / 7.2:
Best and near-best L[subscript p] approximations / 7.3:
Complex variable results for elliptic-type regions / 7.3.1:
Problems for Chapter 7 / 7.4:
Integration Using Chebyshev Polynomials / 8:
Indefinite integration with Chebyshev series / 8.1:
Gauss-Chebyshev quadrature / 8.2:
Quadrature methods of Clenshaw-Curtis type / 8.3:
First-kind formulae / 8.3.1:
Second-kind formulae / 8.3.3:
Third-kind formulae / 8.3.4:
General remark on methods of Clenshaw-Curtis type / 8.3.5:
Error estimation for Clenshaw-Curtis methods / 8.4:
Fitting an exponential curve / 8.4.1:
Other abscissae and polynomials / 8.4.3:
Some other work on Clenshaw-Curtis methods / 8.5:
Problems for Chapter 8 / 8.6:
Solution of Integral Equations / 9:
Fredholm equations of the second kind / 9.1:
Fredholm equations of the third kind / 9.3:
Fredholm equations of the first kind / 9.4:
Singular kernels / 9.5:
Hilbert-type kernels and related kernels / 9.5.1:
Symm's integral equation / 9.5.2:
Regularisation of integral equations / 9.6:
Discrete data with second derivative regularisation / 9.6.1:
Details of a smoothing algorithm (second derivative regularisation) / 9.6.2:
A smoothing algorithm with weighted function regularisation / 9.6.3:
Evaluation of V ([lambda]) / 9.6.4:
Other basis functions / 9.6.5:
Partial differential equations and boundary integral equation methods / 9.7:
A hypersingular integral equation derived from a mixed boundary value problem for Laplace's equation / 9.7.1:
Problems for Chapter 9 / 9.8:
Solution of Ordinary Differential Equations / 10:
A simple example / 10.1:
Collocation methods / 10.2.1:
Error of the collocation method / 10.2.2:
Projection (tau) methods / 10.2.3:
Error of the preceding projection method / 10.2.4:
The original Lanczos tau ([tau]) method / 10.3:
A more general linear equation / 10.4:
Collocation method / 10.4.1:
Projection method / 10.4.2:
Pseudospectral methods--another form of collocation / 10.5:
Definitions / 1:
Preliminary remarks / 1.1:
Trigonometric definitions and recurrences / 1.2:
2.

図書

図書
edited by D.C. Handscomb
出版情報: London ; New York : Academic Press, 1978  xiii, 353 p. ; 24 cm
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3.

図書

図書
J.M. Hammersley and D.C. Handscomb
出版情報: London : Methuen , New York : Wiley, 1964  vii, 178 p. ; 20 cm
シリーズ名: Methuen's monographs on applied probability and statistics
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