Numerical integration in arbitrary-precision ball arithmetic
Idioma
en
Communication dans un congrès
Este ítem está publicado en
Mathematical Software – ICMS 2018, 2018-07-24, Notre Dame. 2018 n° 10931, p. 255–263
Springer
Resumen en inglés
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, ...Leer más >
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.< Leer menos
Palabras clave en inglés
special functions
Numerical integration
interval arithmetic
Orígen
Importado de HalCentros de investigación