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Volume 13 | Issue 8 | Year 2026 | Article Id. IJECE-V13I8P102 | DOI : https://doi.org/10.14445/23488549/IJECE-V13I8P102

GPU Implementation of Parallel Computing Algorithms for Parabolic, Wright, and Riemann Zeta Functions

Chaitanya S. Jage, Vishwesh A. Vyawahare, Mukesh D. Patil

Received Revised Accepted Published
25 Mar 2026 19 May 2026 15 Jul 2026 31 Aug 2026

Citation :

Chaitanya S. Jage, Vishwesh A. Vyawahare, Mukesh D. Patil, "GPU Implementation of Parallel Computing Algorithms for Parabolic, Wright, and Riemann Zeta Functions," International Journal of Electronics and Communication Engineering, vol. 13, no. 8, pp. 26-39, 2026. Crossref, https://doi.org/10.14445/23488549/IJECE-V13I8P102

Abstract

Fast and accurate computation of special functions such as Parabolic function, Wright function and Riemann Zeta function is essential in problems involving fractional calculus, quantum models and large-scale numerical simulations. These functions require extensive series expansions and recurrence-based formulations, which lead to significant computational overhead when computed sequentially. To solve this problem, this work reports the design of optimised parallel computing algorithms for the Parabolic function, Wright function and Riemann Zeta function, and implementation on a Graphics Processing Unit (GPU) platform using Compute Unified Device Architecture (CUDA). The decomposition of these functions substantially speeds up their computation on concurrent CUDA threads, enabling efficient large-scale computation. Techniques to reduce shared memory and strategies to preserve precision are integrated, guaranteeing numerical stability and accuracy in the calculation. The GPU implementation achieves 100x to 160x speed-up over the sequential C implementation, thereby proving the effectiveness of the proposed method for fast and reliable computations of these functions.

Keywords

Parabolic function, Wright function, Riemann Zeta function, Numerical Computation, Parallel Algorithms, CUDA, GPU Computing.

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