The remainder term for analytic functions of Gauss-Lobatto quadratures
نویسندگان
چکیده
منابع مشابه
The remainder term for analytic functions of symmetric Gaussian quadratures
For analytic functions the remainder term of Gaussian quadrature rules can be expressed as a contour integral with kernel Kn. In this paper the kernel is studied on elliptic contours for a great variety of symmetric weight functions including especially Gegenbauer weight functions. First a new series representation of the kernel is developed and analyzed. Then the location of the maximum modulu...
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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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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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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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This paper deals with Vandermonde matrices Vn whose nodes are the Gauss–Lobatto Chebyshev nodes, also called extrema Chebyshev nodes. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both Vn and its inverse and present an explicit formula for the determinant o...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1996
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(96)00100-8