Fast parallel calculation of modified Bessel function of the second kind and its derivatives
Fast parallel calculation of modified Bessel function of the second kind and its derivatives
复制标题
第二类修正贝塞尔函数及其导数的快速并行计算
DOI：
10.1016/j.softx.2021.100923
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发表时间：
2022
期刊：
影响因子：
3.4
通讯作者：
Takashi Takekawa
中科院分区：
文献类型：
--
作者：
Fumiya Tokuhara;Shiho Okinaga;Tetsuhiro Miyahara;Yusuke Suzuki;Tetsuji Kuboyama;Tomoyuki Uchida;松本哲志,正代隆義,内田智之,鈴木祐介,宮原哲浩;Takashi Takekawa
第二类贝塞尔函数的数值计算主要有三种：级数展开、连分式和渐近展开。此外，它们被组合在各自的适当域中。然而，在某些区域，这些类型的组合需要足够的计算时间才能达到足够的精度，然而，并行化时效率显着降低。在该方法中，我们采用了一个简单的数值积分概念，即积分表示。我们预先粗略地细化积分范围，并通过在固定的时间间隔内进行积分计算来稳定计算时间。实验表明，该方法可以在不到一半的计算时间内达到与现有方法相同的精度水平。
There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However, there are some regions where the combination of these types requires sufficient computation time to achieve sufficient accuracy, however, efficiency is significantly reduced when parallelized. In the proposed method, we adopt a simple numerical integration concept of integral representation. We coarsely refine the integration range beforehand, and stabilize the computation time by performing the integration calculation at a fixed number of intervals. Experiments demonstrate that the proposed method can achieve the same level of accuracy as existing methods in less than half the computation time.