Comments on “Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equationA1X1B1+A2X2B2=C”
نویسندگان
چکیده
منابع مشابه
Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$. An $ntimes n$ complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$). In this paper, we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...
متن کاملfinite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$. an $ntimes n$ complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$). in this paper, we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...
متن کاملAnti-reflexive Solutions for a Class of Matrix Equations
In this paper, the generalized anti-reflexive solution for matrix equations (BX = C , XD = E), which arise in left and right inverse eigenpairs problem, is considered. With the special properties of generalized anti-reflexive matrices, the necessary and sufficient conditions for the solvability and a general expression of the solution are obtained. Furthermore, the related optimal approximation...
متن کاملIterative algorithm for the generalized $(P,Q)$-reflexive solution of a quaternion matrix equation with $j$-conjugate of the unknowns
In the present paper, we propose an iterative algorithm for solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} {underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$. By this iterative algorithm, the solvability of the problem can be determined automatically. When the matrix equation is consistent over...
متن کاملGradient Based Iterative Algorithm for Solving the Generalized Coupled Sylvester-transpose and Conjugate Matrix Equations over Reflexive (anti-reflexive) Matrices
Linear matrix equations play an important role in many areas, such as control theory, system theory, stability theory and some other fields of pure and applied mathematics. In the present paper, we consider the generalized coupled Sylvestertranspose and conjugate matrix equations Tν(X) = Fν , ν = 1, 2, . . . , N, where X = (X1, X2, . . . , Xp) is a group of unknown matrices and for ν = 1, 2, . ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2011
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2010.08.018