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1.

図書

図書
Sergey Bagdasarov
出版情報: Basel : Birkhäuser, c1998  xiii, 205 p.
シリーズ名: Operator theory : advances and applications ; v. 105
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2.

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:
3.

図書

図書
J.P. Boyd
出版情報: Berlin ; Tokyo : Springer-Verlag, c1989  xvi, 798 p. ; 25 cm
シリーズ名: Lecture notes in engineering ; 49
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4.

図書

図書
Theodore J. Rivlin
出版情報: New York : Wiley, c1974  vi, 186 p. ; 23 cm
シリーズ名: Pure and applied mathematics
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5.

図書

図書
Theodore J. Rivlin
出版情報: New York : J. Wiley, c1990  xiii, 249 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Definitions and Some Elementary Properties
Extremal Properties
Expansion of Functions in Series of Chebyshev Polynomials
Iterative Properties and Some Remarks About the Graphs of the T n
Some Algebraic and Number Theoretic Properties of the Chebyshev Polynomials
References
Glossary of Symbols
Index
Definitions and Some Elementary Properties
Extremal Properties
Expansion of Functions in Series of Chebyshev Polynomials
6.

図書

図書
L. Fox and I.B. Parker
出版情報: London ; Tokyo : Oxford University Press, 1968  ix, 205 p. ; 22 cm
シリーズ名: Oxford mathematical handbooks
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7.

図書

図書
U. S. Dept. of Commerce. National Bureau of Standards
出版情報: Washington : United States Department of Commerce, National Bureau of Standards ; for sale by the Superintendent of Documents, United States Government Printing Office, 1952  xxix, 161 p. tables ; 27 cm
シリーズ名: National Bureau of Standards applied mathematics series ; 9
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