Chebyshev PolynomialsCRC Press, 2002/09/17 - 360 ページ Chebyshev polynomials crop up in virtually every area of numerical analysis, and they hold particular importance in recent advances 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 focuse |
目次
| 1 | |
2 Basic Properties and Formulae | 19 |
3 The Minimax Property and Its Applications | 41 |
4 Orthogonality and LeastSquares Approximation | 71 |
5 Chebyshev Series | 105 |
6 Chebyshev Interpolation | 145 |
7 NearBest L8734 L1 and Lp Approximations | 165 |
8 Integration Using Chebyshev Polynomials | 177 |
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多く使われている語句
algorithm best approximation bound boundary conditions Chapter Chebyshev expansion Chebyshev polynomials Chebyshev series expansion Clenshaw Clenshaw–Curtis collocation method collocation points computed convergence Corollary cos(n deduce defined Definition derive differential equations differentiation matrices discrete Orthogonality eigenvalues ellipse error evaluate example extrema f(cos finite follows formula four kinds Fourier series Fourier transform fourth-kind function f(x Gauss–Chebyshev give given Hence inner product integral equation kinds of Chebyshev Laurent series Lemma linear equations Lp norm Mason matrix minimax approximation monic polynomials near-best near-minimax norm Note numerical obtain orthogonal polynomials partial sum pn(a pn(x Poisson problem polynomial approximation polynomial interpolation polynomial of degree polynomials Tn problem Proof quadrature recurrence respect second-kind Section sin(n solution solve space spectral methods Table tau method Theorem trigonometric Un(a Un(x values variable vector weight function zeros