求解非线性方程的一个全局收敛算法  

A Global Convergence Method for Solving Nonlinear Equations

作　　者：栾世超[1] 王云诚[2] 

机构地区：[1]曲阜师范大学运筹与管理学院,山东日照276826 [2]山东农业大学信息科学与工程学院,山东泰安271018

出　　处：《鲁东大学学报（自然科学版）》2010年第1期20-22,共3页Journal of Ludong University:Natural Science Edition

摘　　要：首先将求非线性方程的解的问题转化为相应区间上的全局最优化问题,在迭代产生的当前点处通过构建一个辅助函数,并寻求辅助函数的局部极小点,逐步求出非线性方程满足一定精度的解.由此给出了一种求解非线性方程新的全局最优化方法,证明了算法的收敛性,并给出了算法的数值结果.A global optimization method is proposed for finding a solution of a nonlinear equation. The method first converts the problem into a global optimization. Then an auxiliary function is constructed at each present point obtained by the iteration process. A local solution of each auxiliary problem is found by any usable optimization algorithm until it is obtained that a solution satisfied the given precision. Convergence of the algorithm is proved and numerical examples are given.

关 键 词：非线性方程 全局最优化 割峰函数法 

分 类 号：O241.7[理学—计算数学]