Adaptive, Self-Validating Numerical Quadrature

DOI10.1137/0908069zbMath0627.65017OpenAlexW2027772952MaRDI QIDQ3763469

George F. Corliss, Louis B. Rall

Publication date: 1987

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0908069

zbMATH Keywords

singularitiesinterval analysisautomatic differentiationGauss quadratureadaptive quadraturecomparisonsNewton-Cotes quadraturescalar productguaranteed error boundsinterval computationACRITHself-validationroundoff and truncation errorsTaylor series formulas

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical differentiation (65D25)

Related Items (14)

A numerical method for accurately approximating multivariate normal probabilities ⋮ Probability Integrals of the Multivariate t Distribution ⋮ Principles of verified numerical integration ⋮ Survey of integral algorithms for ordinary differential equations ⋮ Set-Membership Computation of Integrals with Uncertain Endpoints ⋮ Error estimates with explicit constants for sinc approximation, sinc quadrature and sinc indefinite integration ⋮ Formally verified approximations of definite integrals ⋮ Automatic differentiation in MATLAB ⋮ Stopping functionals for Gaussian quadrature formulas ⋮ Computing interval enclosures for definite integrals by application of triple adaptive strategies ⋮ Automatic, guaranteed integration of analytic functions ⋮ On the complexity of self-validating numerical integration and approximation of functions with singularities ⋮ Comparison of algorithms for bivariate normal probability over a rectangle based on self-validated results from interval analysis^∗ ⋮ Self-validating integration and approximation of piecewise analytic functions

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