关键词: 非线性方程组, 元胞自动机, 全局收敛性

Abstract: To get all the accurate solutions to Nonlinear Systems of Equations (NSE), the algorithm with global convergence was constructed for solving NSE based on the characteristics of Cellular Automata (CA). In the algorithm, the theoretical search space of NSE was divided into the discrete space, the discrete space was defined as the cellular space; each point in the discrete space was a cell in the cellular space, and each cell was a trial solution of NSE; a cellular state consisted of position and increment of position. The cellular space was divided into many nonempty subsets, and states evolution of all cells from one nonempty subset to another realized the search of the cellular space on the theoretical search space. During evolution process of all cells, each cells transition probability from one position to any another position could be simply calculated; each state of cells during evolution corresponded to a state of a finite Markov chain. The stability condition of a reducible stochastic matrix was used to prove the global convergence of the algorithm. The case study shows that the algorithm is efficient.

Key words: nonlinear systems of equations, cellular automata, global convergence