The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points
نویسندگان
چکیده
منابع مشابه
Generalized Gauss – Radau and Gauss – Lobatto Formulae ∗
Computational methods are developed for generating Gauss-type quadrature formulae having nodes of arbitrary multiplicity at one or both end points of the interval of integration. Positivity properties of the boundary weights are investigated numerically, and related conjectures are formulated. Applications are made to moment-preserving spline approximation. AMS subject classification: 65D30.
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Gauss-Lobatto quadrature formulae associated with symmetric weight functions are considered. The kernel of the remainder term for classes of analytic functions is investigated on elliptical contours. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with either the real or the imaginary axis. The results obtained...
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We derive explicitly the weights and the nodes of the generalized Gauss-Radau and Gauss-Lobatto quadratures with Jacobi weight functions. AMS subject classification: 65D32, 65D30, 41A55.
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When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important poles of the integrand. We describe two methods for generating such quadrature ...
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Rates of convergence (or divergence) are obtained in the application of Gauss, Lobatto, and Radau integration rules to functions with an algebraic or logarithmic singularity inside, or at an endpoint of, the interval of integration. A typical result is the following: For a generalized Jacobi weight function on [-1,1], the error in applying an «-point rule to f(x) = \x -y\~* isO(n~2 + 2i), if y ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1990
ISSN: 0377-0427
DOI: 10.1016/0377-0427(90)90055-5