Please wait a minute...
浙江大学学报(理学版)  2021, Vol. 48 Issue (6): 662-667    DOI: 10.3785/j.issn.1008-9497.2021.06.003
数学与计算机科学     
牛顿-矩阵多分裂多参数TOR迭代法弱收敛性分析
张理涛, 张一帆
郑州航空工业管理学院 数学学院,河南 郑州 450046
Weaker convergence of Newton-matrix nonstationary multisplitting multi-parameters TOR method
ZHANG Litao, ZHANG Yifan
School of Mathematics,Zhengzhou University of Aeronautics, Zhengzhou 450046, Henan, China
 全文: PDF(436 KB)   HTML  
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。
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    
Abstract: 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.
Key words: nonlinear equations    matrix multisplitting method    global relaxed multisplitting multi-parameters method    H-matrix
收稿日期: 2020-10-12 出版日期: 2021-11-25
CLC:  O 242  
基金资助: 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).
作者简介: 张理涛(1980—),ORCID:https://orcid.org/0000-0002-6087-8611,男,博士,教授,主要从事数值代数与科学计算及应用研究,E-mail:litaozhang@163.co;
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  
张理涛
张一帆

引用本文:

张理涛, 张一帆. 牛顿-矩阵多分裂多参数TOR迭代法弱收敛性分析[J]. 浙江大学学报(理学版), 2021, 48(6): 662-667.

ZHANG Litao, ZHANG Yifan. Weaker convergence of Newton-matrix nonstationary multisplitting multi-parameters TOR method. Journal of Zhejiang University (Science Edition), 2021, 48(6): 662-667.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2021.06.003        https://www.zjujournals.com/sci/CN/Y2021/V48/I6/662

1 ORTEGA J M,RHEINBOLDT W C.Iterative Solution of Nonlinear Equations in Several Variables[M].New York:Academic Press,1970. doi:10.1016/b978-0-12-528550-6.50017-x
2 RHEINBOLDT W C.Methods for Solving Systems of Nonlinear Equations[M].Philadelphia:Society for Industrial and Applied Mathematics,1998. doi:10.1137/1.9781611970012
3 AN H B,BAI Z Z.A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations[J]. Applied Numerical Mathematics,2007,57(3):235-252. DOI:10.1016/j.apnum.2006. 02.007
4 安恒斌,白中治. NGLM:一类全局收敛的Newton-GMRES方法[J].计算数学,2005,27(2):151-174. DOI:10.3321/j.issn:0254-7791.2005.02.005 AN H B,BAI Z Z.NGLM:A globally convergent Newton-GMRES method[J].Mathematica Numerica Sinica,2005,27(2):151-174. DOI:10. 3321/j.issn:0254-7791.2005.02.005
5 BROWN P N,SAAD Y.Hybrid Krylov methods for nonlinear systems of equations[J].SIAM Journal on Scientific and Statistical Computing,1990,11(3):450-481. DOI:10.1137/0911026
6 DEMBO R S,EISENSTAT S C,STEIHAUG T.Inexact Newton methods[J].SIAM Journal on Numerical Analysis,1982,19(2):400-408. DOI:10. 1137/0719025
7 EISENSTAT S C,WALKER H F.Globally convergent inexact Newton methods[J].SIAM Journal on Optimization,1994,4(2):393-422. DOI:10.1137/0804022
8 KELLEY C T.Iterative Methods for Linear and Nonlinear Equations[M].Philadelphia:Society for Industrial and Applied Mathematics,1995. DOI:10. 1137/1.9781611970944
9 LEARY D P O,WHITE R E.Multi-splittings of matrices and parallel solution of linear systems[J].SIAM Journal of Algebraic Discrete Methods,1985,6(4):630-640. DOI:10.1137/0606062
10 FROMMER A,MAYER G.Convergence of relaxed parallel multisplitting methods[J].Linear Algebra and Its Applications,1989,119:141-152. DOI:10.1016/0024-3795(89)90074-8
11 WANG D R.On the convergence of parallel multisplitting AOR algorithm[J].Linear Algebra and Its Applications,1991,154/155/156:473-486. DOI:10. 1016/0024-3795(91)90390-I
12 CHANG D W.Convergence analysis of the parallel multisplitting TOR methods[J].Journal of Computational and Applied Mathematics,1996,72(1):169-177. DOI:10.1016/0377-0427(95)00270-7
13 白中治.并行矩阵多分裂迭代算法的收敛速度与发散速度比较[J].工程数学学报,1994,11(1):99-102. BAI Z Z. Comparisons of the convergence and divergence rates of the parallel matrix multisplitting iteration methods [J]. Chinese Journal of Engineering Mathematics, 1994, 11(1): 99-102.
14 CAO Z H,LIN Z Y.Convergence of relaxed parallel multisplitting methods with different weighting schemes[J].Applied Mathematics and Computations,1999,106(2/3):181-196. DOI:10. 1016/S0096-3003(98)10120-0
15 ZHANG L T,HUANG T Z,GU T X,et al.Convergence of relaxed multisplitting USAOR methods for an H-matrices linear systems[J]. Applied Mathematics and Computation,2008,202(1):121-132. DOI:10.1016/j.amc.2008.01.034
16 李建宇.解非线性方程组的牛顿-并行矩阵多分裂算法[J].四川师范大学学报(自然科学版),1995,18(4):51-55. LI J Y. The Newton parallel matrix multisplitting algorithms for solving systems of nonlinear equations[J]. Journal of Sichuan Normal University (Natural Science), 1995, 18(4): 51-55.
17 张理涛,黄廷祝,谷同祥.非线性方程组的牛顿-整体松弛并行多分裂法[J].工程数学学报,2008,25(6):1107-1115. doi:10.3969/j.issn.1005-3085.2008.06.020 ZHANG L T,HUANG T Z,GU T X. Newton-global relaxed parallel multisplitting methods for nonlinear equations[J]. Chinese Journal of Engineering Mathematics, 2008, 25(6):1107-1115. doi:10.3969/j.issn.1005-3085.2008.06.020
18 CHANG D W.The parallel multisplitting TOR (MTOR) method for linear systems[J]. Computers & Mathematics with Applications,2001,41(1/2):215-227. DOI:10.1016/50898-1221(01)85017-3
[1] 高普阳. 三维非牛顿流体充填过程的有限元-间断有限元数值模拟研究[J]. 浙江大学学报(理学版), 2023, 50(1): 49-55.