Linear restriction problem of Hermitian reflexive matrices and its approximation.
ABSTRACT In this paper, we consider a linear restriction problem of Hermitian reflexive matrices and its approximation. By using the properties and structure of Hermitian reflexive matrices and the special properties of reflexive vectors and anti-reflexive vectors, we convert the linear restriction problem to an equivalence problem trickily, which is a special feature of this paper and is a different method from other articles. Then we solve this problem completely and also obtain its optimal approximate solution. Moreover, an algorithm provided for it and the numerical examples show that the algorithm is feasible.
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ABSTRACT: In this paper, The Hermitian reflexive solutions and the anti-Hermitian reflexive solutions of matrix equations AX = B, XC = D are considered. With special properties of partitioned matrices and Hermitian reflexive (anti-Hermitian reflexive) matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is considered.Energy Procedia 01/2012; 17:1591–1597.
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ABSTRACT: A square matrix R is called a generalized reflection matrix iff R=R H and R 2 =I. Let P and Q be two generalized reflexion matrices. From the authors’ abstract: An n×n matrix A is said to be generalized reflexive (generalized anti-reflexive) with respect to the matrix pair (P,Q) if A=PAQ (A=-PAQ). It is obvious that any n×m matrix is also generalized reflexive with respect to the matrix pair (I n ,I m ). By extending the conjugate gradient least squares approach, the present paper treats two iterative algorithms to solve the sytem of matrix equations ℱ i (X)=A i ,i=1,2,⋯,m·Linear Algebra and its Applications 12/2012; 437(11):2793–2812. · 0.97 Impact Factor