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.
CITATION STYLE
Johansson, F. (2018). Numerical Integration in Arbitrary-Precision Ball Arithmetic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10931 LNCS, pp. 255–263). Springer Verlag. https://doi.org/10.1007/978-3-319-96418-8_30
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