High-precision numerical integration: progress and challenges

DOI10.1016/j.jsc.2010.08.010zbMath1291.65070OpenAlexW2052784918WikidataQ56935501 ScholiaQ56935501MaRDI QIDQ540323

Jonathan M. Borwein, David H. Bailey

Publication date: 1 June 2011

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2010.08.010

zbMATH Keywords

numerical integrationquantum field theoryquadraturehigh-precision arithmeticIsing theory

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Parallel numerical computation (65Y05) Numerical integration (65D30)

Related Items (12)

Period computations for covers of elliptic curves ⋮ Fast and Rigorous Arbitrary-Precision Computation of Gauss--Legendre Quadrature Nodes and Weights ⋮ A review note on arbitrary precision arithmetic ⋮ On a hybrid analytical-experimental technique to assess the storage modulus of resilient materials using symbolic computation ⋮ An improved Gregory-like method for 1-D quadrature ⋮ Derivative-based trapezoid rule for the Riemann-Stieltjes integral ⋮ Numerical solution to time-dependent 4D inviscid Burgers' equations ⋮ Improving the Accuracy of the Trapezoidal Rule ⋮ Midpoint derivative-based closed Newton-Cotes quadrature ⋮ Computing periods of hypersurfaces ⋮ The modified composite Gauss type rules for singular integrals using Puiseux expansions ⋮ Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models

Uses Software

• MPI
• ARPREC

Cites Work

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• A high-performance, portable implementation of the MPI message passing interface standard
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• Double exponential formulas for numerical integration
• Parallel integer relation detection: Techniques and applications
• Integrals of the Ising class
• Elliptic integral evaluations of Bessel moments and applications
• A Proof of a Recurrence for Bessel Moments
• Quantum correlations and number theory
• Quantum spin chains and Riemann zeta function with odd arguments
• Hybrid symbolic-numeric integration in multiple dimensions via tensor-product series
• Hypergeometric Forms for Ising-Class Integrals
• A Comparison of Three High-Precision Quadrature Schemes

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