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【期刊论文】ON THE LEAST SQUARES PROBLEM OF A MATRIX EQUATION*1)
廖安平, An-ping Liao
Journal of Computational Mathematics, 17, 6, 1999, 589-594,-0001,():
-1年11月30日
Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered, a new necessary and sufficient condition for solvablity is given, and the expression of solution is derived in the some special cases. Based on the ex-pression, the least spuares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.
Least squares solution, Matrix equation, Inverse eigenvalue problem, Positive semidefinite symmetric matrix.,
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【期刊论文】Least-Squares Solution with the Minimum-Norm for the Matrix Equation (AXB, GXH) = (C, D)
廖安平, AN-PING LIAO* AND YUAN LEI
Computers and Mathematms with Apphcatmns 50(2005)539-549,-0001,():
-1年11月30日
Based on the projection theorem m Hfibert space, by making use of the generahzed singular value decompomtion and the canomcal correlation decomposition, an analytical expression of the least-squares solutmn for the matrix equatmn (AXB, GXH)=(C, D) with the minimum-norm is derived An algorithm for finding the minimum-norm solutmn is described and some numerical results have been given
Matnx equation, Least-squares solution, Urn]mum-norm solutmn, Generahzed singular value decomposltion, Canomcal correlation decomposition
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廖安平, 白中治
计算数学,2002,24(1)9~20,-0001,():
-1年11月30日
By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equa-tion ATXA = D under the restriction that the solution matrix X∈ Rnxn is bisymmetric, where A ∈ Rnxm and D ∈ Rmxm are given matrices.
矩阵方程, 双对称矩阵, 最小二乘解, 标准相关分解
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【期刊论文】线性流形上矩阵方程AX=B的一类反问题及数值解法*1)
廖安平
计算数学,1998,20(4)371~376,-0001,():
-1年11月30日
In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold S={A ∈ SR×n‖AZ-Y‖=min}, the necessary and sufficient conditions for the olvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in [1, 2].
线性流形, 最佳逼近, 反问题, 半正定阵
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廖安平, 张磊, 胡锡炎
数值计算与计算机应用,2000,2:102~111,-0001,():
-1年11月30日
In this paper, four inverse eigenproblems with given three elgenvalues and cor-responding eigenvectors are considered, some necessary and sufficient conditions under which there exists a unique solution for these problems are given. Further-more some numerical algorithms and some numerical experiments are given.
Jacobi matrix, Inverse eigenproblem, Tridiagonal symmetric ma-trix
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