一类非线性方程组的Newton-PSS迭代法
ON NEWTON-PSS METHODS FOR THE SYSTEM OF NONLINEAR EQUATIONS
查看参考文献17篇
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文摘
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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. |
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其他语种文摘
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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. |
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来源
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计算数学
,2012,34(4):329-340 【核心库】
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关键词
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非线性方程组
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正定反Hermite分裂
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不精确Newton方法
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收敛性
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地址
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兰州大学数学与统计学院, 兰州, 730000
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语种
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中文 |
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ISSN
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0254-7791 |
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学科
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数学 |
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基金
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国家973计划
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国家自然科学基金数学天元基金
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文献收藏号
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CSCD:4696239
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参考文献 共
17
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1.
Bai Z Z. A class of two-stage iterative methods for systems of weakly nonlinear equations.
Numer. Algor,1997,14:295-319
|
被引
9
次
|
|
|
|
|
2.
Ortega J M.
Iterative solution of nonlinear equations in several variables,2000
|
被引
11
次
|
|
|
|
|
3.
Rheinboldt W C.
Methods for Solving Systems of Nonlinear Equations,1998
|
被引
4
次
|
|
|
|
|
4.
Dembo R. Inexact Newton methods.
SIAM J. Numer. Anal,1982,19:400-408
|
被引
46
次
|
|
|
|
|
5.
Benzi M. Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods.
Numer. Math,1997,76:309-321
|
被引
6
次
|
|
|
|
|
6.
Deuflhard P.
Newton Methods for Nonlinear Problems,2004
|
被引
2
次
|
|
|
|
|
7.
An H B. A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations.
Appl. Numer. Math,2007,57(3):235-252
|
被引
11
次
|
|
|
|
|
8.
Saad Y.
Iterative Methods for Sparse Linear Systems. 2nd edition,2003
|
被引
6
次
|
|
|
|
|
9.
Bai Z Z. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems.
SIAM J. Matrix Anal. Appl,2002,24:603-626
|
被引
3
次
|
|
|
|
|
10.
杨爱利. 基于多层增量未知元方法的一类三维对流扩散方程的研究.
数学物理学报,2009,29(3):564-572
|
被引
1
次
|
|
|
|
|
11.
Bai Z Z. ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES.
J. Comput. Math,2010,28:235-260
|
被引
6
次
|
|
|
|
|
12.
Bai Z Z. On HSS-based iteration methods for weakly nonlinear systems.
Appl. Numer. Math,2009,59(12):2923-2936
|
被引
9
次
|
|
|
|
|
13.
安恒斌. NGLM:一类全局收敛的Newton-GMRES方法.
计算数学,2005,27(2):151-174
|
被引
5
次
|
|
|
|
|
14.
白中治. 关于Newton-GMRES方法的有效变型与全局收敛性研究.
数值计算与计算机应用,2005,26(4):291-300
|
被引
4
次
|
|
|
|
|
15.
Guo X P. Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations.
Numer. Linear Algebra Appl,2011,18(3):299-315
|
被引
5
次
|
|
|
|
|
16.
Bai Z Z. Block triangular and skew-Hermitian splitting methods for positive-definite linear systems.
SIAM J. Sci. Comput,2005,26:844-863
|
被引
33
次
|
|
|
|
|
17.
Yang A L. A generalized preconditioned HSS method for non-Hermitian positive definite linear systems.
Appl. Math. Comput,2010,216(6):1715-1722
|
被引
6
次
|
|
|
|
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