非线性方程组的牛顿-整体松弛并行多分裂法  

Newton-global Relaxed Parallel Multisplitting Methods for Nonlinear Equations

作　　者：张理涛[1] 黄廷祝[1] 谷同祥[2] 

机构地区：[1]电子科技大学应用数学学院,成都610054 [2]北京应用物理与计算数学研究所,计算物理实验室,北京100088

出　　处：《工程数学学报》2008年第6期1107-1115,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10771030);教育部科技重点项目(107098);电子科大“中青年学术带头人十创新团队”基金;高校博士点专项科研基金(20070614001)

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—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。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.

关 键 词：线性代数方程组 非线性方程组 并行多分裂 整体松弛法 H-矩阵 

分 类 号：O241.6[理学—计算数学]