Extrapolation methods in numerical integration

DOI10.1007/BF02141912zbMath0790.65016OpenAlexW2009827976MaRDI QIDQ688094

Philip Rabinowitz

Publication date: 27 June 1994

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02141912

zbMATH Keywords

singular integralsquadratureextrapolation methodsadaptive extrapolationinfinite range integrals

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (6)

The work of Philip Rabinowitz on numerical integration ⋮ Nonlinear extrapolation estimates of \(\pi\) ⋮ Higher-order weak schemes for the Heston stochastic volatility model by extrapolation ⋮ Asymptotic expansions for trapezoidal type product integration rules ⋮ Computation of irregularly oscillating integrals ⋮ The asymptotic expansion and extrapolation of trapezoidal rule for integrals with fractional order singularities

Uses Software

• QUADPACK
• TRIEX

Cites Work

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• On rates of acceleration of extrapolation methods for oscillatory infinite integrals
• Bessel transforms and rational extrapolation
• Euler-MacLaurin expansions for integrals over triangles and squares of functions having algebraic/logarithmic singularities along an edge
• The Euler-Maclaurin expansion for the Cauchy principal value integral
• A note on an extension of extrapolative techniques for a class of infinite oscillatory integrals
• On quadrature error expansions. I
• Quadrature methods for periodic singular and weakly singular Fredholm integral equations
• Use of Gaussian convergence factors in the numerical evaluation of slowly converging integrals
• Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity
• Comparison of some numerical quadrature formulas for weakly singular periodic Fredholm integral equations
• Quadrature error expansions. II: The full corner singularity
• An Algorithm for Automatic Integration Over a Triangle Using Nonlinear Extrapolation
• A User-Friendly Extrapolation Method for Oscillatory Infinite Integrals
• Extrapolated Adaptive Quadrature
• An extrapolation procedure for the evaluation of singular integrals
• Survey of Extrapolation Processes in Numerical Analysis

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