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arXiv:1802.07942cs.MS

Numerical integration in arbitrary-precision ball arithmetic

Fredrik Johansson

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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.

arXiv comments
8 pages, 1 figure
Journal reference
DOI
Subjects
cs.MSMathematical Software math.NANumerical Analysis

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  1. Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic (2016) 1 comment

    • Author here. I will take the opportunity to advertise my blog at https://fredrikj.net/blog/ where I post occasional development updates about Arb and other projects. Some improvements not covered in the 2016 preprint include much faster code for arithmetic and matrix…

      fdejView on HNParent context

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