一类非线性方程组的Newton-PSS迭代法

doi:10.12286/jssx.2012.4.329

计算数学 ›› 2012, Vol. 34 ›› Issue (4): 329-340.DOI: 10.12286/jssx.2012.4.329

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一类非线性方程组的Newton-PSS迭代法

杨爱利, 伍渝江, 李旭, 孟玲玲

兰州大学数学与统计学院, 兰州 730000

收稿日期:2012-03-10 出版日期:2012-11-15 发布日期:2012-11-12
基金资助:
国家基础研究规划973项目(2011CB706903)和国家自然科学基金天元基金(11026064)资助

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杨爱利, 伍渝江, 李旭, 孟玲玲. 一类非线性方程组的Newton-PSS迭代法[J]. 计算数学, 2012, 34(4): 329-340.

Yang Aili, Wu Yujiang, Li Xu, Meng Lingling. ON NEWTON-PSS METHODS FOR THE SYSTEM OF NONLINEAR EQUATIONS[J]. Mathematica Numerica Sinica, 2012, 34(4): 329-340.

ON NEWTON-PSS METHODS FOR THE SYSTEM OF NONLINEAR EQUATIONS

Yang Aili, Wu Yujiang, Li Xu, Meng Lingling

School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Received:2012-03-10 Online:2012-11-15 Published:2012-11-12

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.

关键词： 非线性方程组, 正定反Hermite分裂, 不精确Newton方法, 收敛性

Positive-definite and skew-Hermitian splitting (PSS) method is an unconditionally convergent 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 systems 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.

Key words: Nonlinear equations, positive and skew-Hermitian splitting, inexact Newton method, convergence property

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一类非线性方程组的Newton-PSS迭代法

ON NEWTON-PSS METHODS FOR THE SYSTEM OF NONLINEAR EQUATIONS

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