中文摘要：

松弛技术是提高分裂迭代法收敛速度的一种基本技术。本文在前人工作的基础上，把求解线性方程组的松弛型矩阵多分裂迭代法推广到了求解非线性方程组，并通过引入多个松弛因子，提出了整体松弛的概念和方法。进而，文中研究了牛顿-整体松弛型矩阵多分裂TOR迭代法，建立了其局部收敛性定理，给出了收敛速度的估计。对于本文提出的求解非线性方程组的牛顿一整体松弛型多分裂TOR迭代法，当选取近似最优参数时，我们的方法将比其他方法有更快的收敛速度。

英文摘要：

The relaxed technique is one of basic skills for improving convergent speed of splitting iterative methods. Based on the current results, this paper extends the relaxed matrix multisplitting TOR iteration method for solving linear systems to that for nonlinear systems and presents the of Newtonglobal relaxed matrix multisplitting methods by introducing some relaxation parameters. Moreover, we study the convergence of our methods, set up convergence theorems and estimate the rate of convergence. If choosing approximately optimal relaxation parameters, our Newton-global relaxed matrix multisplitting TOR iterative methods for nonlinear systems will converge faster than other methods.