牛顿-矩阵多分裂多参数TOR迭代法弱收敛性分析  

Weaker convergence of Newton-matrix nonstationary multisplitting multi-parameters TOR method

作　　者：张理涛[1] 张一帆 ZHANG Litao;ZHANG Yifan(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,Henan,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046

出　　处：《浙江大学学报（理学版）》2021年第6期662-667,共6页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11226337,11501525);河南省高等学校重点科研项目计划基础研究专项(20zx003);河南省高校重点项目(20A110033).

摘　　要：基于非线性方程组的牛顿-全局松弛并行多分裂方法的思想,将求解线性方程组的松弛矩阵多分裂USAOR迭代法推广至求解非线性方程组,研究了牛顿-松弛非定常多分裂多参数TOR迭代法,建立了局部收敛性定理,估计了收敛速度。Based on the ideas of Newton-global relaxation parallel multiple splitting method,this paper extends the applicable equation type of relaxed matrix multisplitting USAOR iterative method from linear systems to nonlinear systems and presents Newton-relaxed nonstationary multisplitting multi-parameters TOR method for nonlinear equations.Moreover,the convergence of this methods are studied,the convergence theorems are set up and the rate of convergence is estimated.

关 键 词：非线性方程组 矩阵多分裂方法 整体松弛多分裂多参数法 H-矩阵 

分 类 号：O242[理学—计算数学]