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一类矩阵方程的正定解研究 被引量：1

Study on Postive Definite Solution of A Class of Matrix Equation
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摘要 研究了矩阵方程X+A*X-1A+B*X-tB=I的正定解.通过构造单调有界迭代序列证明方程存在正定解.提出了一种避免求矩阵逆运算的迭代求解算法.并通过算例说明算法的可行性. The positive definite solution of the matrix equation was investigated in this paper. The existence of the definite solution was proved by constructing monotone bounded iterative sequences. An iteration algorithm was put forward which avoid the operation of matrix inverse. Numerical example was given to illustrate the effectiveness of the method.
作者 崔晓梅
机构地区 吉林化工学院理学院
出处 《吉林化工学院学报》 CAS 2014年第1期108-110,共3页 Journal of Jilin Institute of Chemical Technology
关键词 矩阵方程 正定解 迭代方法 matrix equation iterative consequences positive definite solutions
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献7

  • 1AM.Sarhan,Naglaa M.El-Shazly,Enas M.Shehata. On the existence of extremal positive definite solutions of the nonlinear matrix equationX' + Σmi=1Ai*XδiAi =I[J].{H}Mathematical and Computer Modelling,2010.1107-1117.
  • 2杜忠复.矩阵方程X-A*X^(-α)A-B*X^(-β)B=I的正定解[J].吉林大学学报（理学版）,2010,48(1):26-32. 被引量：8
  • 3廖安平,黄叶楠,沈金荣.矩阵方程X+sum from i=1 to m (A_i~*XV^(-n)A_i=I)的正定解[J].长沙大学学报,2009,23(2):1-4. 被引量：5
  • 4LONG Jian-hui,HU Xi-yan,ZHANG Lei. On the Hermitian positive definite solution of the nonlinear matrix equation X + A* X-1 A + B* X-1 B =I[J].Bull Braz Math Soc New Series,2008,(03):371-386.
  • 5LIU Xin-guo,Gao Hua. On the positive definite solutions of the matrix equations Xs ± ATX-tA =In[J].{H}Linear Algebra and its Applications,2003.83-97.
  • 6M.Parodi. La localisation des valeurs caracterisiques des matrices et ses Application[M].Gauthiervillars Paris,1959.
  • 7Furuta. Operator inequalities associated with HolderMccarthy and Kantorovich inequalities[J].I Inequal Appl,1998,(06):137-148.

二级参考文献15

  • 1Anderson W N, et al. Positive solutions to X = A - BX^-1 B^*[J]. Linear Algebra Appl. , 1990,(134) :53 -62.
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共引文献8

同被引文献6

  • 1A.M.Sarhan,Naglaa M.El-Shazly,Enas M.Shehata,On the existence of extremal positive definite solutions of the nonlinear matrix equation Xr+∑mi=1A*iXδiAi=I[J].Mathematical and Computer Modelling,2010,51:1107-1117.
  • 2Xin-Guo Liu,Hua Gao,On the positive definite solutions of the matrix equations Xs±ATX-tA=In[J].Linear Algebra and its Application,2003,368:83-97.
  • 3Jian-hui Long,Xi-yan Hu,Lei Zhang.On the Hermitian positive definite solution of the nonlinear matrix equation X+A*X-1A+B*X-1B=I[J].Bull Braz Math Soc,New Series 2008,39(3):371-386.
  • 4M.Parodi,La localisation des valeurs caracterisiques des matrices etses Application[M].Gauthiervillars,Paris 1959.
  • 5X.Zhan.Computing the extremal positive definite solutions of a matrix equation[J].SIAM J.Sci.Comput.,1996(17):1167-1174.
  • 6廖安平,黄叶楠,沈金荣.矩阵方程X+sum from i=1 to m (A_i~*XV^(-n)A_i=I)的正定解[J].长沙大学学报,2009,23(2):1-4. 被引量：5

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吉林化工学院学报
2014年 第1期

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