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Mohammadi, Seyed Mohsen, Etesami, Reza, Madadi, Mohsen. (1404). Optimizing Closed-Form Approximations of the Error Function via the Gaussian Combined Arms Metaheuristic. , 57(2), 150-169. doi: 10.22059/jac.2026.409129.1251
Seyed Mohsen Mohammadi; Reza Etesami; Mohsen Madadi. "Optimizing Closed-Form Approximations of the Error Function via the Gaussian Combined Arms Metaheuristic". , 57, 2, 1404, 150-169. doi: 10.22059/jac.2026.409129.1251
Mohammadi, Seyed Mohsen, Etesami, Reza, Madadi, Mohsen. (1404). 'Optimizing Closed-Form Approximations of the Error Function via the Gaussian Combined Arms Metaheuristic', , 57(2), pp. 150-169. doi: 10.22059/jac.2026.409129.1251
Mohammadi, Seyed Mohsen, Etesami, Reza, Madadi, Mohsen. Optimizing Closed-Form Approximations of the Error Function via the Gaussian Combined Arms Metaheuristic. , 1404; 57(2): 150-169. doi: 10.22059/jac.2026.409129.1251

Optimizing Closed-Form Approximations of the Error Function via the Gaussian Combined Arms Metaheuristic

Journal of Algorithms and Computation
دوره 57، شماره 2، اسفند 2025، صفحه 150-169    اصل مقاله (560.33 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/jac.2026.409129.1251
نویسندگان
Seyed Mohsen Mohammadi1؛ Reza Etesami2؛ Mohsen Madadi* 2
1Shahid Bahonar University of Kerman
2Shahid Bahonar University of Kerman, Kerman, Iran
چکیده
The error function, erf(x), is crucial in many fields but lacks a closed-form solution. To improve existing closed-form approximations, this paper introduces a global-optimization framework that refines their numerical coefficients without changing their analytical form. The optimization minimizes a composite objective of mean and maximum absolute error (MAE and Max-AE) over selected domains. We solve this using the Gaussian Combined Arms (GCA) metaheuristic. For 16 structural types, the method often reduces error by an order of magnitude while maintaining formula simplicity and low cost. We also present new, highly accurate approximations with closed-form inverses. The framework is a powerful, transferable tool for enhancing approximations of erf(x) and related functions.
کلیدواژه‌ها
closed-form approximation؛ coefficient tuning؛ numerical refinement؛ inverse error function؛ function optimization
آمار
تعداد مشاهده مقاله: 54
تعداد دریافت فایل اصل مقاله: 43





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