AbstractConsider the nonlinear matrix equation X-A∗X-pA=Q with 0<p⩽1. This paper shows that there exists a unique positive definite solution to the equation. A perturbation bound and the backward error of an approximate solution to this solution is evaluated. We also obtain explicit expressions of the condition number for the unique positive definite solution. The theoretical results are illustrated by numerical examples
AbstractIn this paper we study the matrix equation X=Q+A∗(X̂−C)−1A, where Q is an n×n positive defin...
AbstractSimple necessary and sufficient conditions for the matrix equation X + ATX−1A = I to have a ...
AbstractThe two matrix equations Xs+ATX−tA=In and Xs−ATX−tA=In are studied. Based on the fixed-point...
AbstractIn this paper, the nonlinear matrix equation Xs+A∗X-tA=Q is investigated. Necessary conditio...
AbstractIn this paper we investigate nonlinear matrix equations X+A*X−qA=Q and X−A*X−qA=Q where q∈(0...
AbstractIn this paper we investigate nonlinear matrix equations X±A∗X−qA=Q where q≥1. We derive nece...
AbstractA conjecture that the nonlinear matrix equation X−∑i=1mAi∗XrAi=Q(−1≤r<0 or 0<r<1) always has...
AbstractConsider the nonlinear matrix equationX+A∗X−1A=P,where A,P are n×n complex matrices with P H...
AbstractIn this paper, the nonlinear matrix equation X+A∗F(X)A=Q is discussed. Sufficient conditions...
AbstractIn this paper we investigate the nonlinear matrix equation X+ATX−1A=P, for the existence of ...
AbstractIn this paper we consider the positive definite solutions of nonlinear matrix equation X+A⋆X...
AbstractConsider the nonlinear matrix equationX+A∗X−1A=P,where A, P are n×n complex matrices with P ...
AbstractConsider the nonlinear matrix equation X-A∗X-pA=Q with 0<p⩽1. This paper shows that there ex...
AbstractThe Hermitian positive definite solutions of the matrix equation X+A*X−2A=I are studied. A n...
AbstractBased on fixed point theorems for monotone and mixed monotone operators in a normal cone, we...
AbstractIn this paper we study the matrix equation X=Q+A∗(X̂−C)−1A, where Q is an n×n positive defin...
AbstractSimple necessary and sufficient conditions for the matrix equation X + ATX−1A = I to have a ...
AbstractThe two matrix equations Xs+ATX−tA=In and Xs−ATX−tA=In are studied. Based on the fixed-point...
AbstractIn this paper, the nonlinear matrix equation Xs+A∗X-tA=Q is investigated. Necessary conditio...
AbstractIn this paper we investigate nonlinear matrix equations X+A*X−qA=Q and X−A*X−qA=Q where q∈(0...
AbstractIn this paper we investigate nonlinear matrix equations X±A∗X−qA=Q where q≥1. We derive nece...
AbstractA conjecture that the nonlinear matrix equation X−∑i=1mAi∗XrAi=Q(−1≤r<0 or 0<r<1) always has...
AbstractConsider the nonlinear matrix equationX+A∗X−1A=P,where A,P are n×n complex matrices with P H...
AbstractIn this paper, the nonlinear matrix equation X+A∗F(X)A=Q is discussed. Sufficient conditions...
AbstractIn this paper we investigate the nonlinear matrix equation X+ATX−1A=P, for the existence of ...
AbstractIn this paper we consider the positive definite solutions of nonlinear matrix equation X+A⋆X...
AbstractConsider the nonlinear matrix equationX+A∗X−1A=P,where A, P are n×n complex matrices with P ...
AbstractConsider the nonlinear matrix equation X-A∗X-pA=Q with 0<p⩽1. This paper shows that there ex...
AbstractThe Hermitian positive definite solutions of the matrix equation X+A*X−2A=I are studied. A n...
AbstractBased on fixed point theorems for monotone and mixed monotone operators in a normal cone, we...
AbstractIn this paper we study the matrix equation X=Q+A∗(X̂−C)−1A, where Q is an n×n positive defin...
AbstractSimple necessary and sufficient conditions for the matrix equation X + ATX−1A = I to have a ...
AbstractThe two matrix equations Xs+ATX−tA=In and Xs−ATX−tA=In are studied. Based on the fixed-point...
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