修正的第二类贝塞尔函数及其导数的快速并行计算
Fast parallel calculation of modified Bessel function of the second kind and its derivatives
摘要：
第二类贝塞尔函数的数值计算主要有三种类型：级数展开、连分数和渐近展开。此外，它们在各自的适当域中进行组合。然而，在某些区域中，这些类型的组合需要足够的计算时间来实现足够的精度，然而，并行化时效率显著降低。在所提出的方法中，我们采用了一个简单的数值积分概念的整表示。我们预先粗略地细化积分范围，并通过以固定数量的间隔执行积分计算来稳定计算时间。实验表明，该方法可以达到相同的精度水平，现有的方法在小于一半的计算时间。
英文摘要：
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.
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