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Least-Squares Solutions of Generalized Sylvester Equation with Xi Satisfies Different Linear Constraint
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作者 Xuelin Zhou Dandan Song +1 位作者 Qingle Yang Jiaofen Li 《Advances in Linear Algebra & Matrix Theory》 2016年第2期59-74,共16页
In this paper, an iterative method is constructed to find the least-squares solutions of generalized Sylvester equation , where is real matrices group, and satisfies different linear constraint. By this iterative meth... In this paper, an iterative method is constructed to find the least-squares solutions of generalized Sylvester equation , where is real matrices group, and satisfies different linear constraint. By this iterative method, for any initial matrix group within a special constrained matrix set, a least squares solution group with  satisfying different linear constraint can be obtained within finite iteration steps in the absence of round off errors, and the unique least norm least-squares solution can be obtained by choosing a special kind of initial matrix group. In addition, a minimization property of this iterative method is characterized. Finally, numerical experiments are reported to show the efficiency of the proposed method. 展开更多
关键词 Least-Squares Problem Centro-Symmetric matrix bisymmetric matrix Iterative Method
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THE SOLVABILITY CONDITIONS FOR THE INVERSE PROBLEM OF BISYMMETRIC NONNEGATIVE DEFINITE MATRICES 被引量:18
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作者 Dong-xiu Xie Lei Zhang Xi-yan Hu 《Journal of Computational Mathematics》 SCIE CSCD 2000年第6期597-608,共12页
A = (a[sub ij]) ∈ R[sup n×n] is termed bisymmetric matrix if a[sub ij] = a[sub ji] = a[sup n ? j + 1, n ? i + 1], i, j = 1, 2 ··· n. We denote the set of all n x n bisymmetric matrices by BSR[sup ... A = (a[sub ij]) ∈ R[sup n×n] is termed bisymmetric matrix if a[sub ij] = a[sub ji] = a[sup n ? j + 1, n ? i + 1], i, j = 1, 2 ··· n. We denote the set of all n x n bisymmetric matrices by BSR[sup n x n]. This paper is mainly concerned with solving the following two problems: Problem I. Given X, B ∈ R[sup n×m], find A ∈ P[sub n] such that AX = B, where P[sub n] = {A ∈ BSR[sup n×n]| x[sup T] Ax ≥ 0, ?x ∈ R[sup n]}. Problem II. Given A[sup *] ∈ R[sup n×n], find ? ∈ S[sub E] such that ||A[sup *] - ?||[sub F] = ... ||A[sup *] - A||[sub F] where || · ||[sub F] is Frobenius norm, and S[sub E] denotes the solution set of problem I. The necessary and sufficient conditions for the solvability of problem I have been studied. The general form of S[sub E] has been given. For problem II the expression of the solution has been provided. [ABSTRACT FROM AUTHOR] 展开更多
关键词 Frobenius norm bisymmetric matrix the optimal solution
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A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications 被引量:9
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作者 QingWenWANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第2期323-334,共12页
We consider the system of four linear matrix equations A_1 X = C_1,XB_2 =C_2,A_3,XB_3, = C3 and A_4XB_4 = C_4 over R, an arbitrary von Neumann regular ring with identity. Anecessary and sufficient condition for the ex... We consider the system of four linear matrix equations A_1 X = C_1,XB_2 =C_2,A_3,XB_3, = C3 and A_4XB_4 = C_4 over R, an arbitrary von Neumann regular ring with identity. Anecessary and sufficient condition for the existence and the expression of the general solution tothe system are derived. As applications, necessary and sufficient conditions are given for thesystem of matrix equations A_1X = C_1 and A_3X = C_3 to have a bisymmetric solution, the system ofmatrix equations A_1X = C_1 and A_3XB_3 = C_3 to have a perselfconjugate solution over R with aninvolution and char R≠2, respectively. The representations of such solutions are also presented.Moreover, some auxiliary results on other systems over R are obtained. The previous known results onsome systems of matrix equations are special cases of the new results. 展开更多
关键词 von Neumann regular ring system of matrix equations perselfconjugatematrix centrosymmetric matrix bisymmetric matrix
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The Constrained Solutions of Two Matrix Equations 被引量:41
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作者 An Ping LIAO Zhong Zhi BAI Department of Mathematics. Hunan University. Changshu, 410082. P. R. China Department of Mathematics and Information Science, Changsha University, Changsha 410003. P. R. China Academy of Mathematics and System. Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. China State Key Laboratory of Scientific/Engineering Computing. Chinese Academy of Sciences. Institute of Computational Mathematics and Scientific/Engineering Computing. Academy of Mathematics and System Sciences. Chinese Academy of Sciences. P. O. Box 2719. Beijing 100080. P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2002年第4期671-678,共8页
We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with... We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with m, n, p positive integers: and the bisymmetric positive semidefinite solution of the matrix equation D^T XD=C, where D is a given real n×m matrix. C is a given real m×m matrix, with m. n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions. 展开更多
关键词 matrix equation Symmetric positive semidefinite matrix bisymmetric positive semidefinite matrix
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