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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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【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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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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廖安平, Liao An-ping Zhang Lei
A Journal of Chinese Universities, 1998, Vol. 7, No.2, 195-200,-0001,():
-1年11月30日
Consider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and su f ficent conditions for the solvability, as well as the general solution are obtained. The best approa'imate solution by the above solution set is given. Thus the open problem in [1] is solved.
Matrix inverse problem, symmetric positive semidefinite matrix, best approzimate so-lution
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【期刊论文】矩阵方程AXAT+BYBT=C的对称与反对称最小范数最小二乘解*1)
廖安平, 白中治
计算数学,2005,27(1)81~95,-0001,():
-1年11月30日
对于任意给定的矩阵A ∈Rkxn,B ∈Rkxn 和C ∈Rkxk,利用奇异值分解和广义奇异分解,我们给出了矩阵方程AXAT+BYBT=C的对称与反对称最小范数最小二乘解的表达式。
对称矩阵, 反对称矩阵, 奇异值分解, 广义奇异值分解, 最小范数解, 最小二乘解
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