文章基本信息

标题：An elementary proof that real roots nonexistence of nonlinear equations and its optimal solutions
本地全文：下载
作者：Li Lanyou ; Lux Jingui ; Jianhong Chen 等
期刊名称：MATEC Web of Conferences
电子版ISSN：2261-236X
出版年度：2018
卷号：175
DOI：10.1051/matecconf/201817503036
语种：English
出版社：EDP Sciences
摘要：In this paper, we give an elementary proof that the real roots nonexistence of nonlinear equation such as: xn+yn+zn=n,where n =1,2,3,(x,y,z)∈ℝ by contradiction. Thus, when n takes all positive integers between 4 and 1981, the value of function f= xn+yn+znbased on the exact solution of the above equations is still real. Finally, numerical experiments presents a set of approximate numerical solutions by using standard genetic algorithm(SGA), adaptive particle swarm optimization algorithm(APSO) and artificial fish swarm algorithm(AFSA).