ALGORITHM-707 - CONHYP - A NUMERICAL EVALUATOR OF THE CONFLUENT HYPERGEOMETRIC FUNCTION FOR COMPLEX ARGUMENTS OF LARGE MAGNITUDES

被引:25
作者
NARDIN, M
PERGER, WF
BHALLA, A
机构
[1] UNIV MICHIGAN,DEPT ELECT ENGN,ANN ARBOR,MI 48109
[2] MICHIGAN TECHNOL UNIV,DEPT ELECT ENGN,HOUGHTON,MI 49931
来源
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | 1992年 / 18卷 / 03期
关键词
CONFLUENT HYPERGEOMETRIC; SPECIAL FUNCTIONS; EVALUATOR;
D O I
10.1145/131766.131774
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
A numerical evaluator for the confluent hypergeometric function for complex arguments with large magnitudes using a direct summation of Kummer's series is presented. Extended precision subroutines using large arrays to accumulate a single numerator and denominator are ultimately used in a single division to arrive at the final result. The accuracy has been verified through a variety of tests and they show the evaluator to be consistently accurate to 13 significant figures, and on rare occasion accurate to only 9 for magnitudes of the arguments ranging into the thousands in any quadrant in the complex plane. Because the evaluator automatically determines the number of significant figures of machine precision, and because it is written in FORTRAN 77, tests on various computers have shown the evaluator to provide consistently accurate results, making the evaluator very portable. The principal drawback is that, for certain arguments, the evaluator is slow; however, the evaluator remains valuable as a benchmark even in such cases.
引用
收藏
页码:345 / 349
页数:5
相关论文
共 3 条
[1]  
ABRAMOWITZ M, 1972, HDB MATH FUNCTIONS F, P390
[2]  
NADIN M, 1992, J COMPUT APPL MATH, V39, P193
[3]  
SLATER LJ, 1960, CONFLUENT HYPERGEOME, P58