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矩阵方程A_1Z+ZB_1=C_1的广义自反最佳逼近解的迭代算法

AN ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE OPTIMAL APPROXIMATION SOLUTIONS OF MATRIX EQUATIONS A_1Z + ZB_1 = C_1
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摘要 本文研究了Sylvester复矩阵方程A_1Z+ZB_1=c_1的广义自反最佳逼近解.利用复合最速下降法,提出了一种的迭代算法.不论矩阵方程A_1Z+ZB_1=C_1是否相容,对于任给初始广义自反矩阵Z_0,该算法都可以计算出其广义自反的最佳逼近解.最后,通过两个数值例子,验证了该算法的可行性. In this paper, we present an iterative algorithm to calculate the optimal approximation solutions of the Sylvester complex matrix equations A1Z ＋ ZB1 = C1 over generalized reflexive （anti-reflexive） matrices by using the hybrid steepest descent method. Whether matrix equations A1Z ＋ ZB1 = C1 are consistent or not, for arbitrary initial reflexive （anti-reflexive） matrix Z0, the given algorithm can be used to compute the reflexive （anti-reflexive） optimal approximation solutions. The effectiveness of the proposed algorithm is verified by two numerical examples.
作者 杨家稳 孙合明
机构地区 滁州职业技术学院基础部 河海大学理学院
出处 《数学杂志》 CSCD 北大核心 2014年第5期968-976,共9页 Journal of Mathematics
基金 安徽省教育厅自然科学基金资助(KJ2011B119)
关键词 Sylvester矩阵方程 KRONECKER积 复合最速下降法 最佳逼近 广义自反矩阵 Sylvester matrix equations Kronecker product hybrid steepest descent method optimal approximation reflexive matrix
分类号 O241.6 [理学—计算数学]
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参考文献9

  • 1Chen Hsinchu. Generalized reflexive matrices: special properties and applications [J]. SIAM J.Matrix Anal Appl., 1998(19): 140-153.
  • 2Chen Hsinchu, Ahmed H SAMEH. Numerical linear algebra algorithms on the cedar system [A].Noor A K (Ed.). Parallel computations and their impact on mechanics[C]. The American Society ofMechanical Engineers, 1987,86 : 101—125.
  • 3Chen Hsinchu. The SAS domain decomposition method for structural analysis[R]. CSRD Teach,report 754, Center for Supercomputing Research and Development, Urbana, IL: University of Illinois,1988.
  • 4Peng Z Y, Hu X Y. The reflexive and anti-reflexive solutions of matrix equation AX = B [J]. LinearAlgebra Appl., 2003 (375): 147—155.
  • 5Peng Xiangyang, Hua Xiyan, Zhang Lei. The reflexive and anti-reflexive solutions of the matrixequation [J]. Journal of Computational and Applied Mathematics, 2007 (200): 749-760.
  • 6Xu Weiwei, Li Wen. The Hermitian reflexive solutions to the matrix inverse problem [J]. AppliedMathematics and Computation, 2009, (211): 142-147.
  • 7张忠志,胡锡炎,张磊.线性约束下反Hermitian广义反Hamiltonian矩阵的最佳逼近问题[J].工程数学学报,2004,21(F12):88-92. 被引量：3
  • 8Yamada I. The hybrid steepest descent method for the variational inequality problem over theintersection of fixed point sets of nonexpansive mappings [A]. Butnariu D,Censor Y, Reich S (Eds.).Inherently parallel algorithm for feasibility and optimization and their applications[C]. Elsevier,2001.
  • 9Yamada I, Ogura N,Shirakawa N. A numerically robust hybrid steepest descent method for theconvexly constrained generalized inverse problems [J]. Contemporary Mathematics, 2002 (313): 269-305.

二级参考文献7

  • 1谢冬秀,张磊.一类反对称阵反问题的最小二乘解[J].工程数学学报,1993,10(4):25-34. 被引量：79
  • 2孙继广.实对称矩阵的两类逆特征值问题[J].计算数学.1988(03)
  • 3Ben-Israel A,Greville T N E.Generalized Inverse: Theory and Applications[]..1974
  • 4Boley D,Golub G H.A survey of matrix inverse eigenvalue problems[].Inverse Problems.1987
  • 5Li N,chu K W E.Designing the llopfield neural network via pole assignment[].Internat J Systems Sci.1994
  • 6Xie Dong-Xiu.Least-Squares solution for inverse eigenpair problem of nonnegative definite matrices[].Computers and Mathematics With Applications.2000
  • 7谢冬秀,张磊,胡锡炎.一类双对称矩阵反问题的最小二乘解[J].计算数学,2000,22(1):29-40. 被引量：69

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数学杂志
2014年 第5期

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