Approximations of the modified Bessel functions of the second kind K_ν. Applications in random field generation

2023/03/23 by D. I. Palade, Palade, D. I., L. M. Pomârjanschi +1
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Financial Risk and Volatility Modeling #Mathematical Physics (math-ph) #Soil Geostatistics and Mapping #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2303.13400

openalex publication_date 2023/03/23 · openalex created_date 2023/03/25 · openalex updated_date 2026/07/28

Abstract

We propose an analytical approximation for the modified Bessel function of the second kind K_ν. The approximation is derived from an exponential ansatz imposing global constrains. It yields local and global errors of less than one percent and a speed-up in the computing time of 3 orders in magnitude in comparison with traditional approaches. We demonstrate the validity of our approximation for the task of generating long-range correlated random fields.

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