منابع مشابه
Quadrature formulae of non-standard type
We discuss quadrature formulae of highest algebraic degree of precision for integration of functions of one or many variables which are based on non-standard data, i.e., in which the information used is different from the standard sampling of function values. Among the examples given in this survey is a quadrature formula for integration over the disk, based on linear integrals on n chords, whi...
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In this paper we obtain certain generalizations of the trapezoidal rule and the Euler-Maclaurin formula that involve derivatives. In the case of quadrature of functions of exponential type over infinite intervals we find conditions under which existence of the (improper) integral and convergence of the approximating series become equivalent. In the process, we also establish a best possible ver...
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The general Euler two-point formulae are used with functions possessing various convexity and concavity properties to derive inequalities pertinent to numerical integration.
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The aim of this paper is to generalize inequality 0096-3 doi:10 * Co E-m f ðxÞ 1 b a Z b a f ðs1Þds1 f ðbÞ f ðaÞ b a x aþ b 2 f 0ðbÞ f 0ðaÞ 2ðb aÞ x 2 ðaþ bÞxþ a 2 þ b þ 4ab 6 6 kf k1 ðb aÞ 3 6 I x a b a obtained in [A. Aglić Aljinović, M. Matić, J. Pečarić, Improvements of some Ostrowski type inequalities, J. Comput. Anal. Appl., in press], and therefore obtain a generalization and improvement...
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In recent years a number of authors have considered an error analysis for quadrature rules of Newton-Cotes type. In particular, the mid-point, trapezoid and Simpson rules have been investigated more recently ([2], [4], [5], [6], [11]) with the view of obtaining bounds on the quadrature rule in terms of a variety of norms involving, at most, the first derivative. In the mentioned papers explicit...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2009
ISSN: 1331-4343
DOI: 10.7153/mia-12-45