Fast computation of a general complete elliptic integral of third kind by half and double argument transformations
作者：
Highlights：
• We developed a new method to compute the associate complete elliptic integral of the third kind, J(n|m).
• The method utilizes the double argument formula of J(n|m) with respect to n.
• The errors of the new method is sufficiently small as around 10 machine epsilons.
• The new method is 20%–50% faster than Bulirsch’s cel.
• The new method is around 5 times faster than Carlson’s RJ.
摘要
Highlights•We developed a new method to compute the associate complete elliptic integral of the third kind, J(n|m).•The method utilizes the double argument formula of J(n|m) with respect to n.•The errors of the new method is sufficiently small as around 10 machine epsilons.•The new method is 20%–50% faster than Bulirsch’s cel.•The new method is around 5 times faster than Carlson’s RJ.
论文关键词：Complete elliptic integral,Double argument transformation,Half argument transformation
论文评审过程：Received 18 January 2013, Revised 5 April 2013, Available online 15 April 2013.
论文官网地址：https://doi.org/10.1016/j.cam.2013.04.015
