基于偏序集不动点理论的矩阵方程可解性研究（英文）
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摘要
首先构造了一个偏序集中的新的不动点定理,然后基于此不动点定理,证明了矩阵方程X-mΣi=1A_i~*X~(δi)A_i=Q(0<δ_i<1)总是存在唯一的Hermite正定解.
In this paper, a new fixed point theorem in partially order sets is proposed. Based on this fixed point theorem, we proved that the matrix equation X-mΣiA_i~*X~(δi)A_i = Q(0 < δ_i < 1) always has a unique Hermitian positive definite(HPD) solution without any restrictions on coefficient matrices.
In this paper, a new fixed point theorem in partially order sets is proposed. Based on this fixed point theorem, we proved that the matrix equation X-mΣiA_i~*X~(δi)A_i = Q(0 < δ_i < 1) always has a unique Hermitian positive definite(HPD) solution without any restrictions on coefficient matrices.
引文
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[8]Li J.Perturbation analysis of the nonlinear matrix equation X-(?)A_i~*X~(pi)A_i=Q[J].Abstract and Applied Analysis,2013,2013:979832.
[9]Duan X F,Wang Q W,Li C M.Perturbation analysis for the positive definite solution of the nonlinear matrix equation X-(?)A_i~*X~(δi)A_i=Q[J].Journal of Applied Mathematics&Informatics,2012,30:655-663.
[10]Duan X F,Liao A P,Tang B.On the nonlinear matrix equation X-(?)A_i~*X~(δi)A_i=Q[J].Linear Algebra and its Applications,2008.429:110-121.
[11]Lim Y.Solving the nonlinear matrix equation X=Q+(?)M_iX~(δi)M_i~*via a contraction principal[J].Linear Algebra and its Applications,2009,430:1380-1383.
[12]Parodi M,Villat H.La Localisation Des Valeurs Caracterisiques Desmatrices Etses Applications[M].Paris:Gauthiervillars,1959.
[2]Anderson W N,Kleindorfer G B,Kleindorfer M B,et al.Consistent estimates of the parameters of a linear systems[J].The Annals of Mathematical Statistics,1969,40:2064-2075.
[3]Bucy R S.A priori bounds for the Riccati equation[C].Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability,Vol.Ⅲ:Probability Theory,Berkeley:University of California Press,1972.
[4]Ouellette D V.Schur complements and statistics[J].Linear Algebra and its Applications,1981,36:187-295.
[5]Pusz W,Woronowitz S L.Functional calculus for sequlinear forms and purification map[J].Reports on Mathematical Physics,1975,8:159-170.
[6]Anderson W N,Morley T D,Trapp G E.The cascade limit,the shorted operator and quadratic optimal control[C].Linear Circuits,Systems and Signal Processsing:Theory and Application,1988.
[7]Buzbee B L,Golub G H,Nielson C W.On direct methods for solving Poisson's equations[J].SIAM Journal on Numerical Analysis,1970,7:627-656.
[8]Li J.Perturbation analysis of the nonlinear matrix equation X-(?)A_i~*X~(pi)A_i=Q[J].Abstract and Applied Analysis,2013,2013:979832.
[9]Duan X F,Wang Q W,Li C M.Perturbation analysis for the positive definite solution of the nonlinear matrix equation X-(?)A_i~*X~(δi)A_i=Q[J].Journal of Applied Mathematics&Informatics,2012,30:655-663.
[10]Duan X F,Liao A P,Tang B.On the nonlinear matrix equation X-(?)A_i~*X~(δi)A_i=Q[J].Linear Algebra and its Applications,2008.429:110-121.
[11]Lim Y.Solving the nonlinear matrix equation X=Q+(?)M_iX~(δi)M_i~*via a contraction principal[J].Linear Algebra and its Applications,2009,430:1380-1383.
[12]Parodi M,Villat H.La Localisation Des Valeurs Caracterisiques Desmatrices Etses Applications[M].Paris:Gauthiervillars,1959.