Modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices

被引：0
作者：
Min-Hong Chen
Qing-Biao Wu
机构：
[1] Zhejiang Sci-Tech University,Department of Mathematics
[2] Zhejiang University,Department of Mathematics
来源：
Numerical Algorithms | 2019年 / 80卷
关键词：
Splitting iteration; Modified Newton-MDPMHSS method; Large sparse nonlinear system; Block two-by-two complex symmetric matrices; Local convergence analysis; 65F10; 65F50; 65H10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this study, an efficient iterative method is given to solve large sparse nonlinear systems with block two-by-two complex symmetric Jacobian matrices. Based on the double-parameter preconditioned MHSS (DPMHSS) method, a modified double-parameter preconditioned MHSS (MDPMHSS) method is developed to solve a class of linear systems with block two-by-two complex coefficient matrices. Then, a modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices is obtained, which MDPMHSS is employed as the inner iteration and the modified Newton method is employed as the outer iteration. Local convergence analysis is given for the new present method under Hölder condition, which is weaker than Lipschitz condition. At last, numerical results are reported to verify the efficiency of the new method.
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页码：355 / 375
页数：20
相关论文
共 66 条
[1]  
Dembo RS(1982)Inexact Newton methods SIAM J. Numer. Anal. 19 400-408
[2]  
Eisenstat SC(2007)A choice of forcing terms in inexact Newton method J. Comput. Appl. Math. 200 47-60
[3]  
Steihaug T(2008)A convergence theorem for the inexact Newton methods based on Hölder continuous Fréchet derivative Appl. Math. Comput. 197 206-211
[4]  
An H-B(2009)Kantorovich-type convergence criterion for inexact Newton methods Appl. Numer. Math. 59 1599-1611
[5]  
Mo Z-Y(2007)A globally convergent newton-GMRES method for large sparse systems of nonlinear equations Appl. Numer. Math. 57 235-252
[6]  
Liu X-P(2004)Jacobian-free Newton-Krylov method: a survey of approaches and applications J. Comput. Phys. 193 357-397
[7]  
Zhou J-L(2010)On newton-HSS methods for systems of nonlinear equations with positive-definite Jacobian matrices J. Comput. Math. 28 235-260
[8]  
Zhang S-Y(2012)Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices Numer. Algebra, Control Optim. 2 839-853
[9]  
Yang G-P(2014)Accelerated newton-GPSS methods for systems of nonlinear equations J. Comput. Anal. Appl. 17 245-254
[10]  
Tan J(2007)A third-order Newton-type method to solve systems of nonlinear equations Appl. Math. Comput. 187 630-635
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