Computing Special Functions by Using Quadrature Rules |
| |
Authors: | Amparo Gil Javier Segura Nico M Temme |
| |
Institution: | (1) Departamento de Matemáticas, U. Autónoma de Madrid, 28049- Madrid, Spain;(2) Departamento de Matemáticas, Estadística y Computación, U. de Cantabria, 39005 Santander, Spain;(3) CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands |
| |
Abstract: | The usual tools for computing special functions are power series, asymptotic expansions, continued fractions, differential equations, recursions, and so on. Rather seldom are methods based on quadrature of integrals. Selecting suitable integral representations of special functions, using principles from asymptotic analysis, we develop reliable algorithms which are valid for large domains of real or complex parameters. Our present investigations include Airy functions, Bessel functions and parabolic cylinder functions. In the case of Airy functions we have improvements in both accuracy and speed for some parts of Amos's code for Bessel functions. |
| |
Keywords: | numerical computation of special functions numerical quadrature steepest descent method saddle point method Airy functions Bessel functions |
本文献已被 SpringerLink 等数据库收录! |
|