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.

翻译：第二类贝塞尔函数的数值计算有三种主要类型:序列扩展、连续分数和零星扩展,此外,它们被合并到适合每个类型的领域;然而,有些区域,这些类型的综合计算需要足够的计算时间来实现足够的准确性,但是,在平行化时,效率会大大降低;在拟议方法中,我们采用一个简单数字集成的整体代表概念;我们事先粗略地改进整合范围,并通过以固定间隔次数进行集成计算来稳定计算时间;实验表明,在不到一半的计算时间内,拟议方法可以达到与现有方法相同的精确度。