Numerical integration in arbitrary-precision ball arithmetic

Fredrik Johansson 1
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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https://hal.inria.fr/hal-01714969
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Submitted on : Thursday, February 22, 2018 - 10:11:03 AM
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Fredrik Johansson. Numerical integration in arbitrary-precision ball arithmetic. Mathematical Software – ICMS 2018, James H. Davenport and Manuel Kauers and George Labahn and Josef Urban, Jul 2018, Notre Dame, United States. pp.255-263, ⟨10.1007/978-3-319-96418-8_30⟩. ⟨hal-01714969⟩

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