关于Brown方法的半局部收敛性

On the Semi-local Convergence of Brown's Method

在本文中,我们讨论解非线性方程组的Brown方法的半局部收敛性。通过对Brown方法的算法结构作深入的分析,我们将Brown方法变换成带有特殊误差项的近似Newton法,基于这种等价变形,我们建立了Brown方法的半局部收敛定理,从而完善了Brown方法的收敛理论。

In this paper, we discuss the semi-local convergence with regional estimation of Brown's method for solving systems of nonlinear equations. Through the deep anaysis on the algorithm structure of Brown's metkod, we convert 'Brown's method into an approximate Newtoh's method. Based on-such equivalent variation, we establish the semi-local convergence theorem of Brwn's method, which is a complement of the convergence theory of Brown's method.