一类非线性方程组的Newton-PSS迭代法  

ON NEWTON-PSS METHODS FOR THE SYSTEM OF NONLINEAR EQUATIONS

作　　者：杨爱利[1] 伍渝江[1] 李旭[1] 孟玲玲[1] 

机构地区：[1]兰州大学数学与统计学院,兰州730000

出　　处：《计算数学》2012年第4期329-340,共12页Mathematica Numerica Sinica

基　　金：国家基础研究规划973项目(2011CB706903);国家自然科学基金天元基金(11026064)资助

摘　　要：正定反Hermite分裂(PSS)方法是求解大型稀疏非Hermite正定线性代数方程组的一类无条件收敛的迭代算法.将其作为不精确Newton方法的内迭代求解器,我们构造了一类用于求解大型稀疏且具有非Hermite正定Jacobi矩阵的非线性方程组的不精确Newton-PSS方法,并对方法的局部收敛性和半局部收敛性进行了详细的分析.数值结果验证了该方法的可行性与有效性.Positive-definite and skew-Hermitian splitting （PSS） method is an unconditionally con- vergent iterative method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of PSS iteration as the inner solver of inexact Newton method, we establish a class of inexact Newton-PSS methods for solving large sparse sys- tems of nonlinear equations with positive-definite Jacobian matrices at the solution points. The local and semilocal convergence properties are analyzed under some proper assumptions. Numerical results are given to examine the feasibility and effectivity of inexact Newton-PSS methods.

关 键 词：非线性方程组 正定反Hermite分裂 不精确Newton方法 收敛性 

分 类 号：O241.6[理学—计算数学]