MATEC Web Conf.
Volume 175, 20182018 International Forum on Construction, Aviation and Environmental Engineering-Internet of Things (IFCAE-IOT 2018)
|Number of page(s)||5|
|Section||Computer Simulation and Design|
|Published online||02 July 2018|
An elementary proof that real roots nonexistence of nonlinear equations and its optimal solutions
School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing Jiangsu 211800, China
2 Office of Information Construction and Management, Nanjing Institute of Technology, Nanjing Jiangsu 211167, China
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+zn based 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).
© The Authors, published by EDP Sciences 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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