Characterization of Functions in Terms of Rate of Convergence of a Quadrature Process

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1991Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 111, page 85 (issn: 0002-9939,

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Authors: Rahman, Q. I.; Schmeisser, G.;

doi: 10.2307/2047864 , 10.1090/s0002-9939-1991-1045597-0

Characterization of Functions in Terms of Rate of Convergence of a Quadrature Process

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Abstract

We discuss the relationship between the regularity properties of a continuous 2 π 2\pi -periodic function f f and the behavior of the remainder of the trapezoidal rule on [ 0 , 2 π ] [0,2\pi ] applied to f f .

Keywords

trapezoidal rule, regularity properties, Rate of convergence, degree of approximation, Topological linear spaces of continuous, differentiable or analytic functions, Numerical quadrature and cubature formulas, Approximate quadratures

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