Numerical integration in arbitrary-precision ball arithmetic
Langue
en
Communication dans un congrès
Ce document a été publié dans
Mathematical Software – ICMS 2018, 2018-07-24, Notre Dame. 2018 n° 10931, p. 255–263
Springer
Résumé en anglais
We present an implementation of arbitrary-precision numerical integration with rigorous error bounds in the Arb library. Rapid convergence is ensured for piecewise complex analytic integrals by use of the Petras algorithm, ...Lire la suite >
We present an implementation of arbitrary-precision numerical integration with rigorous error bounds in the Arb library. Rapid convergence is ensured for piecewise complex analytic integrals by use of the Petras algorithm, which combines adaptive bisection with adaptive Gaussian quadrature where error bounds are determined via complex magnitudes without evaluating derivatives. The code is general, easy to use, and efficient, often outperforming existing non-rigorous software.< Réduire
Mots clés en anglais
special functions
Numerical integration
interval arithmetic
Origine
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