منابع مشابه
Generalized Chebyshev Interpolation and Its Application to Automatic Quadrature
A generalized Chebyshev interpolation procedure increasing a fixed number of sample points at a time is developed and analyzed. It is incorporated into an efficient automatic quadrature scheme of Clenshaw-Curtis type. Numerical examples indicate that the present method is efficient not only for well-behaved functions but for those with discontinuous low order derivatives by virtue of adequate e...
متن کاملAlmost - Interpolatory Chebyshev Quadrature
The requirement that a Chebyshev quadrature formula have distinct real nodes is not always compatible with the requirement that the degree of precision of an npoint formula be at least equal to n. This condition may be expressed as | \d\ \p = 0, 1 g p, where d (dx, ■ ■ ■ , d„) with Mo(w) ~ , -IT dj = 2w A iM ; = 1, 2, • • ■ , z!, ZJ ,_, Pj(io), j = 0, 1, • • • , are the moments of the weight fu...
متن کاملOn computing rational Gauss-Chebyshev quadrature formulas
We provide an algorithm to compute the nodes and weights for Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary real poles outside [−1, 1]. Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the complexity is of...
متن کاملRational Interpolation at Chebyshev points
The Lanczos method and its variants can be used to solve eeciently the rational interpolation problem. In this paper we present a suitable fast modiication of a general look-ahed version of the Lanczos process in order to deal with polynomials expressed in the Chebyshev orthogonal basis. The proposed approach is particularly suited for rational interpolation at Chebyshev points, that is, at the...
متن کاملAutomatic differentiation of quadrature
We analyse the application of automatic differentiation (AD) to the quadrature (numerical integration) of a function integrand to determine the sensitivities of the integral to variation in the limits of integration. We derive an expression for the truncation errors of such ADderived sensitivities and relate them to the truncation error of the original, and a closely related, function quadratur...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1988
ISSN: 0898-1221
DOI: 10.1016/0898-1221(88)90179-4