Year: 1994
Author: Xi-Yan Hu, Lei Zhang, Wei-Zhang Du
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 1 : pp. 78–87
Abstract
This paper studies the following two problem:
Problem Ⅰ. Given $X,B∈R^{n×m}$, find $A∈P_{s,n}$, such that $AX=B$, where
$P_{s,n}$={$A∈SR^{n×n}|x^T AX≥0，∀S^Tx=0$ , for given $S∈R^{n×p}_p$}.
Problem Ⅱ. Given $A^*∈R^{n×n}$, find $\hat{A}∈S_E$, such that $||A^*-\hat{A}||$=inf$_{A∈S_E}||A^*-A||$ where $S_E$ denotes the solutions set of Problem Ⅰ.
The necessary and sufficient conditions for the solvability of Problem Ⅰ, the expression of the general solution of Problem Ⅰ and the solution of Problem Ⅱ are given for two case. For the general case, the equivalent form of conditions for the solvability of Problem Ⅰ is given.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1994-JCM-10229
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 1 : pp. 78–87
Published online: 1994-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10