Numerical integration in arbitrary-precision ball arithmetic
This work provides a practical, efficient tool for rigorous numerical integration, benefiting researchers and engineers who require high-precision computations with guaranteed error bounds.
The paper presents an implementation of arbitrary-precision numerical integration with rigorous error bounds in the Arb library, using the Petras algorithm to achieve rapid convergence for piecewise complex analytic integrals. The code is general, easy to use, and often outperforms existing non-rigorous software.
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.