Precise and fast computation of Jacobian elliptic functions by conditional duplication

被引：6

作者：

Fukushima, Toshio ^{[1
]}

机构：

[1] Natl Inst Nat Sci, Natl Astron Observ Japan, Mitaka, Tokyo 1818588, Japan

来源：

NUMERISCHE MATHEMATIK | 2013年 / 123卷 / 04期

关键词：

HALF; KIND;

D O I：

10.1007/s00211-012-0498-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We developed a new method to compute the cosine amplitude function, , by using its double argument formula. The accumulation of round-off errors is effectively suppressed by the introduction of a complementary variable, , and a conditional switch between the duplication of and . The sine and delta amplitude functions, and , are evaluated from thus computed or by means of their identity relations. The new method is sufficiently precise as its errors are less than a few machine epsilons. Also, it is significantly faster than the existing procedures. In case of single precision computation, it runs more than 50 times faster than Bulirsch's sncndn based on the Gauss transformation and 2.7 times faster than our previous method based on the simultaneous duplication of and . The ratios change to 7.6 and 3.5 respectively in case of the double precision environment.

引用

页码：585 / 605

页数：21

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