@Article{JCM-21-4,
author = {Zhen-Yun, Peng and Xi-Yan, Hu and Zhang, Lei},
title = {The Inverse Problem for Part Symmetric Matrices on a Subspace},
journal = {Journal of Computational Mathematics},
year = {2003},
volume = {21},
number = {4},
pages = {505--512},
abstract = {<p style="text-align: justify;">In this paper, the following two problems are considered:<br/>Problem Ⅰ. Given $S \in R^{n×p}, X, B \in R^{n×m}$, find $A \in SR_{s,n}$ such that $AX=B$, where $SR_{s,n}={A \in R^{n×n} | x^T(A-A^T)=0, \ {\rm for} \ {\rm all} \ x \in R(S)}$.</p><p style="text-align: justify;">Problem Ⅱ. Given $A^* \in R^{n×n}$, find $\hat{A} \in S_E$ such that $\|\hat{A} -A^*\|={\rm min}_{A \in S_E} \|A-A*\|$, where $S_E$ is the solution set of Problem Ⅰ.</p><p style="text-align: justify;">Then necessary and sufficient conditions for the solvability of and the general from of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided.</p><p><br/></p>},
issn = {1991-7139},
doi = {https://doi.org/2003-JCM-10254},
url = {https://global-sci.com/article/85343/the-inverse-problem-for-part-symmetric-matrices-on-a-subspace}
}