数学与计算机科学 |
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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 |
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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 |
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 |
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