A circular interpretation of the Euler-Maclaurin formula.

DOI10.1016/j.cam.2005.02.015zbMath1086.65002OpenAlexW2034402196MaRDI QIDQ818193

Jean-Paul Berrut

Publication date: 24 March 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.02.015

zbMATH Keywords

numerical examplesBernoulli polynomialstrapezoidal ruledefinite integralEuler-Maclaurin formulaRiemann sumerror formula

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Euler-Maclaurin formula in numerical analysis (65B15)

Related Items (9)

An extension of trapezoidal type product integration rules ⋮ Extrapolation quadrature from equispaced samples of functions with jumps ⋮ A formula for the error of finite sinc interpolation with an even number of nodes ⋮ Asymptotic behaviors of intermediate points in the remainder of the Euler-Maclaurin formula ⋮ A formula for the error of finite sinc-interpolation over a finite interval ⋮ Fourier and barycentric formulae for equidistant Hermite trigonometric interpolation ⋮ A fourth order product integration rule by using the generalized Euler-Maclaurin summation formula ⋮ The Influence of Jumps on the Sinc Interpolant, and Ways to Overcome It ⋮ First applications of a formula for the error of finite sinc interpolation

Cites Work

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• End-point corrected trapezoidal quadrature rules for singular functions
• A practical guide to splines
• Computational Techniques Based on the Lanczos Representation
• Numerical Integration of Periodic Functions: A Few Examples
• The Splitting Extrapolation Method
• The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula. III. Functions having algebraic singularities

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