一类算子方程的正算子解问题的研究
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摘要
研究算子方程Xs+A*X-t A=Q的正算子解的存在性问题.通过构造有效的迭代序列,给出算子方程Xs+A*X-t A=Q有正算子解的一些必要条件和充分条件;利用空间分解和算子分块的方法,给出了不同方程解之间的关系.
In this paper,the positive operator solutions to operator equation Xs+A*X-t A=Q were studied.Firstly,by constructing effective iterative sequence,the necessary conditions and sufficient conditions for the existence of positive operator solutions to the operator equation Xs+A*X-t A =Q were derived respectively.Secondly,using space decomposition and operator block,the relations of solutions to different operator equation was studied.
In this paper,the positive operator solutions to operator equation Xs+A*X-t A=Q were studied.Firstly,by constructing effective iterative sequence,the necessary conditions and sufficient conditions for the existence of positive operator solutions to the operator equation Xs+A*X-t A =Q were derived respectively.Secondly,using space decomposition and operator block,the relations of solutions to different operator equation was studied.
引文
[1] YANG Y,DUAN F,ZHAO X.On solutions for the matrix equation Xs+A*X-t A=Q[C]//Proc of the Seventh Int Conf on Matrix Theory and Its Applications in China,2006:21-24.
[2] VEJDI I,HASANO V.Positive definite solutions of the matrix equations X±A*X-q A=Q[J].Linear Algebra Appl,2005,404(53):166-182.
[3] El-SAYED S M,RAN A C M.On an iteration method for solving a class of nonlinear matrix equations[J].SIAM J Matrix Anal,2001,26(23):632-645.
[4] HASANOV V I,El-SAYED S M.On the positive definite solutions for nonlinear matrix equation X+A*X-δA=Q[J].Linear Algebra Appl,2006,5412(42):154-160.
[5] CONWAY J B.A course in functional analysis[M].New York:Springer-Verlag,1990.
[6] GUSTAFSON K E,RAO D K M.Numerical range[M].New York:Springer-Verlag,1997.
[7]杨凯凡,张文鹏,窦艳妮.一类算子方程的正算子解[J].西北大学学报(自然科学版),2014,101(4):537-539.
[8]王少英,田学刚.算子方程(X*)n X+X*An=B的解[J].西南大学学报(自然科学版),2010,32(8):138-141.
[2] VEJDI I,HASANO V.Positive definite solutions of the matrix equations X±A*X-q A=Q[J].Linear Algebra Appl,2005,404(53):166-182.
[3] El-SAYED S M,RAN A C M.On an iteration method for solving a class of nonlinear matrix equations[J].SIAM J Matrix Anal,2001,26(23):632-645.
[4] HASANOV V I,El-SAYED S M.On the positive definite solutions for nonlinear matrix equation X+A*X-δA=Q[J].Linear Algebra Appl,2006,5412(42):154-160.
[5] CONWAY J B.A course in functional analysis[M].New York:Springer-Verlag,1990.
[6] GUSTAFSON K E,RAO D K M.Numerical range[M].New York:Springer-Verlag,1997.
[7]杨凯凡,张文鹏,窦艳妮.一类算子方程的正算子解[J].西北大学学报(自然科学版),2014,101(4):537-539.
[8]王少英,田学刚.算子方程(X*)n X+X*An=B的解[J].西南大学学报(自然科学版),2010,32(8):138-141.