Recent software developments for special functions in the Santander-Amsterdam project

被引：1

作者：

Gil, Amparo ^{[1
]}

Segura, Javier ^{[2
]}

Temme, Nico M. ^{[3
,4
]}

机构：

[1] Univ Cantabria, ETSI Caminos, Dept Matemat Aplicada & Ciencias Computac, E-39005 Santander, Spain

[2] Univ Cantabria, Dept Matemat Estadist & Computac, E-39005 Santander, Spain

[3] IAA, NL-1391 VD Abcoude 18, Netherlands

[4] CWI, NL-1098 XG Amsterdam, Netherlands

来源：

SCIENCE OF COMPUTER PROGRAMMING | 2014年 / 90卷

关键词：

Special functions; Incomplete gamma functions; Marcum's Q-function; Zeros of special functions; Numerical software; NUMERICALLY SATISFACTORY SOLUTIONS; CYLINDER FUNCTIONS U(A; X); COMPLEX AIRY FUNCTIONS; FORTRAN-77; ROUTINES; GAMMA-FUNCTION RATIOS; IMAGINARY ORDERS; BESSEL-FUNCTIONS; COMPUTATION; ALGORITHM; ZEROS;

D O I：

10.1016/j.scico.2013.11.004

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We give an overview of published algorithms by our group and of current activities and future plans. In particular, we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we describe the recent developments for the computation of central and non-central chi-square cumulative distributions (also called Marcum Q-functions), and we present a new quadrature method for computing them. Secondly, we describe the fourth-order methods for computing zeros of special functions recently developed, and we provide an explicit example for the computation of complex zeros of Bessel functions. We end with an overview of published software by our group for computing special functions. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：42 / 54

页数：13

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