Fast parallel calculation of modified Bessel function of the second kind and its derivatives

TL;DR

This paper introduces a fast parallel method for computing the modified Bessel function of the second kind and its derivatives using a numerical integration approach, significantly reducing computation time while maintaining accuracy.

Contribution

A novel parallel computation method based on integral representation that improves efficiency over traditional techniques for Bessel functions.

Findings

Achieves same accuracy as existing methods

Reduces computation time by more than half

Effective in parallel computing environments

Abstract

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.