Quadrature Formulae and Polynomial Inequalities
نویسندگان
چکیده
منابع مشابه
Integro-differential polynomial and trigonometrical splines and quadrature formulae
This work is one of many that are devoted to the further investigation of local interpolating polynomial splines of the fifth order approximation. Here, new polynomial and trigonometrical basic splines are presented. The main features of these splines are the following; the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed ...
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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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In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.
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Abstract. It is well-known that the trapezoidal rule, while being only second-order accurate in general, improves to spectral accuracy if applied to the integration of a smooth periodic function over an entire period on a uniform grid. More precisely, for the function that has a square integrable derivative of order r the convergence rate is o ( N−(r−1/2) ) , where N is a number of grid nodes. ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1997
ISSN: 0021-9045
DOI: 10.1006/jath.1996.3080