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Numerical Integration in Arbitrary-Precision Ball Arithmetic

  • Fredrik Johansson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

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.

Keywords

Numerical integration Interval arithmetic Special functions 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LFANT – INRIA – IMBBordeauxFrance

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