A Comparison of Three High-Precision Quadrature Schemes

DOI10.1080/10586458.2005.10128931zbMath1082.65028OpenAlexW2137946669MaRDI QIDQ5717427

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Publication date: 9 January 2006

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1128371757

zbMATH Keywords

performanceerror estimatesnumerical examplesnumerical quadratureEuler-Maclaurin summation formulaarbitrary precisionarbitrary precision (ARPREC) software package

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Complexity and performance of numerical algorithms (65Y20) Euler-Maclaurin formula in numerical analysis (65B15)

Related Items (21)

Jonathan Borwein: Experimental Mathematician ⋮ Fast algorithms using orthogonal polynomials ⋮ Box integrals ⋮ Pentagon functions for scattering of five massless particles ⋮ Very accurate time propagation of coupled Schrödinger equations for femto- and attosecond physics and chemistry, with C++ source code ⋮ On computational applications of the Levi-Civita field ⋮ Numerical computation of endomorphism rings of Jacobians ⋮ A note on nonparametric inference for species variety with Gibbs-type priors ⋮ \textit{TimeEvolver}: a program for time evolution with improved error bound ⋮ High-precision computation: mathematical physics and dynamics ⋮ On the Morse index of higher-dimensional free boundary minimal catenoids ⋮ Adaptive numerical integration of exponential finite elements for a phase field fracture model ⋮ Computation and theory of extended Mordell-Tornheim-Witten sums ⋮ High-precision numerical integration: progress and challenges ⋮ Advances in the theory of box integrals ⋮ Computation and Experimental Evaluation of Mordell–Tornheim–Witten Sum Derivatives ⋮ A numerical scheme for the one-dimensional wave equation subject to an integral conservation condition ⋮ Computing the moment polynomials of the zeta function ⋮ Pentagon functions for one-mass planar scattering amplitudes ⋮ Computation and theory of Mordell-Tornheim-Witten sums. II. ⋮ Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models

Uses Software

• ARPREC
• Algorithm 719

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