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变预处理子SOR-双共轭残量法 被引量：4

A Variable Preconditioning SOR-Biconjugate Residual Algorithm
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摘要 研究了大规模稀疏线性方程组的预条件迭代求解算法。结合Krylov子空间方法和SOR迭代,给出了一个新的求解算法,即变预处理子SOR-双共轭残量法,同时给出了算法的收敛性分析。数值实验显示了算法的快速收敛性。 In this paper, the preconditioning iterative method of large sparse linear systems has been considered. Combining Krylov subspace methods with SOR, a new algorithm of the preconditioning SOR -biconjugate residual algorithm has been proposed. Meanwhile, the convergence analysis has been presented. The numerical experiments showed that the new algorithm exhibited fast convergence performance.
作者 汪祥 聂永明 李乐波
机构地区 南昌大学数学系
出处 《南昌大学学报（工科版）》 CAS 2011年第3期281-284,289,共5页 Journal of Nanchang University(Engineering & Technology)
基金 国家自然科学基金资助项目(10961010) 江西省自然科学基金资助项目(2010GZS0137)
关键词 大规模稀疏线性方程组 预处理子 SOR迭代 双共轭残量法 large sparse linear systems preconditioner SOR iteration bi-conjugate residual algorithm
分类号 O241.6 [理学—计算数学]
  • 相关文献

参考文献12

  • 1汪祥,李乐波.对称Toeplitz线性方程组的基于余弦变换的最佳预优矩阵[J].数值计算与计算机应用,2010,31(3):223-231. 被引量：1
  • 2SAAD Y. Iterative methods for sparse linear system [ M ]. Boston : PWS, 1996.
  • 3SAAD Y. A flexible inner-outer preconditioned GMRES Algorithm [ J ]. Siam J Sci Stat Comput, 1993,14 ( 2 ) : 469 - 493.
  • 4VORST H A, VUIK C. GMRESR: A family of nested GMRES methods [ J ]. Numer Linear Algebra Appl, 1994, 1(4) :369-386.
  • 5SAAD Y, SCHULTZ M H. GMRES:A generalized minimal residual algorithm for solving nonsymmetric linear systems [ J ]. SIAM J Sci stat Comput, 1986,7 (3) : 856 - 869.
  • 6ABE K,ZHANG S L. A variable preconditioning using the SOR Method for GCR-like methods[ J]. Int J Numer Anal Model ,2005,2 (2) : 147 - 16.
  • 7AXELSSON O. A generalized conjugate gradient least square method [ J ]. Numer Math, 1987,51 ( 2 ) : 209 - 227.
  • 8AXELSSON O, VASSILEVSKI P S. A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning [ J ]. SIAM J Numer Anal, 1991,12(4) :625 -644.
  • 9GOLUB H G, YE Q. Inexact preconditioned conjugate gradient method with inner-outer iteration [ J ]. SIAM J Sci Comput, 1999,21 (4) : 1305 - 1320.
  • 10SZYLD D B, YOGEL J A. FQMR:a flexible quasi-minimal residual method with inexact preconditioning [ J ]. SIAM J Sci Stat Comput,2001,23(2) :363 -380.

二级参考文献13

  • 1Boman E, Koltracht I. Fast transform bused preconditioners for Toeplitz equations[J]. SIAM J. Matrix Anal. Appl., 1995, 16: 628-645.
  • 2Cai M, Jin X. A note on T.Chan's preconditioner[J]. Linear Algebra and Its Applications, 2004, 376: 283-290.
  • 3Cai M, Jin X, Wei Y. A generalization of T. Chan's preconditioner[J]. Linear Algebra and Its Applications, 2005, 407: 11-18.
  • 4Chan T. An optimal circulant preconditioner for Toeplitz systems[J]. SIAM J. Sci. Statist. Comput., 1988, 9: 766-711.
  • 5Chan R, Wrong C. Best conditioned circulant preconditioners[J]. Linear Algebra Appl., 1995, 218: 205-212.
  • 6Chan R, Ng M. Sine transform based preconditioners for symmetric toeplitz systems[J]. Linear Algebra Appl., 1996, 232: 237-259.
  • 7Chan R, Yip A, Ng M. The best circulant preconditioners for Hermitian Toeplitz matrices[J]. SIAM J. Numer. Anal., 2001, 38: 876-896.
  • 8Chan R, Ng M, Yip A. The best circulant preconditioners for Hermitian Toeplitz systems II: the multiple-zero case[J]. Numer. Math., 2002, 92: 17-40.
  • 9Cheng C, Jin X. Some stability properties of T. Chan's preconditioner[J]. Linear Algebra and Its Applications, 2005, 395: 361-365.
  • 10Huckle T. Circulant and skew-circulant matrices for solving Toeplitz matrix problems[J]. SIAM J. Matrix Anal. Appl., 1992, 13: 767-777.

同被引文献19

  • 1白中治.并行矩阵多分裂块松弛迭代算法[J].计算数学,1995,17(3):238-252. 被引量：21
  • 2COTYLE R W, PANG J S, STONE R E. The linear com- plementarity problem [ M ]. Academic Press : San Diego, 1992.
  • 3BAI Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems [ J ]. Numerical Linear Algebra with Applications,2010,17:917 - 933.
  • 4LEENAERTS D M W, VAN B W. Piecewise linear model- ing and analysis [ M ]. Kluwer Academic Publishers : Doro drecht, 1998.
  • 5MURTY K G. Linear complementarity, linear and nonlin- ear programming [ M ]. Helderma nn-Verlag: Berlin, 1988.
  • 6DONG J L, JIANG M Q. A modified modulus method for symmetric positive-definite linear complementarity prob- lems [ J ]. Numerical Linear Algebra with Applications 2009,16 : 129 - 143.
  • 7BAI Z Z, ZHANG L L. Modulus-based synchronous two: stage mnltisplitting iteration methods for linear comple- mentarity problems [ J ]. Numer. Algorithms,2013,62 ( 1 ) : 59 - 77.
  • 8BAI Z Z, MIGALL6N V, PENAD6S J, et al. Block and a- synchronous two-stage methods for mildly nonlinear sys- tems[ J]. Numer Math, 1999,82 : 1 - 20.
  • 9BAI Z Z, EVANS D J. Matrix mnltisplitting methods with applications to linear eomplementarity problems: parallel synehronous and chaotic methods [ J ]. R6seaux et Syst:mes R6partis : Caleulateurs Parallel:s, 2001,13 : 125 - 154.
  • 10BAI Z Z, EVANS D J. Matrix multisplitting relaxation methods for linear complementarity problems [ J ]. Interna- tional Journal of Computer Mathematics, 1997,63 : 309 - 326.

引证文献4

二级引证文献6

南昌大学学报（工科版）
2011年 第3期

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