Numerical integration in arbitrary-precision ball arithmetic
Language
en
Communication dans un congrès
This item was published in
Mathematical Software – ICMS 2018, 2018-07-24, Notre Dame. 2018 n° 10931, p. 255–263
Springer
English 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, ...Read more >
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.Read less <
English Keywords
special functions
Numerical integration
interval arithmetic
Origin
Hal imported