Article

# Linear restriction problem of Hermitian reflexive matrices and its approximation.

College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China

Applied Mathematics and Computation (Impact Factor: 1.6). 06/2008; 200:341-351. DOI: 10.1016/j.amc.2007.11.020 Source: DBLP

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**ABSTRACT:**In the present paper, we consider the minimum norm solutions of the general least squares problem By developing the conjugate gradient least square (CGLS) method, we construct an efficient iterative method to solve this problem. The constructed iterative method can compute the solution group of the problem within a finite number of iterations in the absence of roundoff errors. Also it is shown that the method is stable and robust. Finally, by some numerical experiments, we demonstrate that the iterative method is effective and efficient. Copyright © 2013 John Wiley & Sons, Ltd.Mathematical Methods in the Applied Sciences 11/2013; · 0.78 Impact Factor - [Show abstract] [Hide abstract]

**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. - [Show abstract] [Hide abstract]

**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. · 0.98 Impact Factor

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