Еволюційний метод апроксимації функцій дійсними поліномами

• Дата: 2023
• Автори: Козак, Олег, Самотий, Володимир, Павельчак, Андрій
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2023
• Теми: поліном з дійсними степенями; апроксимація функцій; неперіодичні сигнали; генетичні алгоритми; алгоритми оптимізації; параметрична оптимізація.
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/347
• Назва журналу: Physico-mathematical modeling and informational technologies

This paper proposes a hybrid method for determining the coefficients of a polynomial whosepower coefficients are real numbers using a genetic algorithm (GA). The input is a set of discretevalues of the function arguments. The main focus of our approach is to approximate functionsusing real polynomials, which provide more flexibility compared to cubic polynomials. Ourapproach involves a two-step optimization process. In the first step, the power coefficients of thepolynomial are equal to cubic polynomial powers. Then approximation coefficients of the cubicpolynomial are calculated using GA. In the second step, instead of cubic polynomial is introducedpolynomial with real powers. In this step the approximation coefficients of polynomial are set asconstant and power coefficients of polynomial are calculated using GA to refine the solution. Thismakes it possible to quickly and accurately approximate a given function with a polynomial whosepowers are real numbers. The evolutionary nature of the method ensures adaptability and theability to overcome functional obstacles, thus achieving better overall approximationperformance. Research has shown that, compared to conventional polynomials, significantlyhigher approximation accuracy has been achieved.