On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures
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.
متن کاملGeneralized Gauss-Radau and Gauss-Lobatto formulas with Jacobi weight functions
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.
متن کاملOn Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae
Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the present note we show the positivity of the corresponding weights; this positivity has been conjectured already by Gautschi. As a consequence, we establish several ...
متن کاملOn the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions
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...
متن کاملThe 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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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1991
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181073004