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2009年03月30日

【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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2009年03月30日

【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

摘要

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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2009年03月30日

【期刊论文】三对角对称矩阵逆特征问题存在唯一解的条件*1)

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

摘要

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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2009年03月30日

【期刊论文】THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE SOLVABILITY OF A CLASS OF THE MATRIX INVERSE PROBLEM*

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

摘要

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