Numerical integration in arbitrary-precision ball arithmetic
Mathematical Software
2018-02-23 v1 Numerical Analysis
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
Cite
@article{arxiv.1802.07942,
title = {Numerical integration in arbitrary-precision ball arithmetic},
author = {Fredrik Johansson},
journal= {arXiv preprint arXiv:1802.07942},
year = {2018}
}
Comments
8 pages, 1 figure