@Article{JCM-12-1,
author = {Xi-Yan, Hu and Zhang, Lei and Wei-Zhang, Du},
title = {The Solvability Conditions for the Inverse Problem of Matrices Positive Semidefinite on a Subspace},
journal = {Journal of Computational Mathematics},
year = {1994},
volume = {12},
number = {1},
pages = {78--87},
abstract = {<p style="text-align: justify;">This paper studies the following two problem:<br/>Problem&nbsp;Ⅰ. Given $X,B∈R^{n×m}$, find $A∈P_{s,n}$, such that $AX=B$, where <br/>$P_{s,n}$={$A∈SR^{n×n}|x^T AX≥0，∀S^Tx=0$ , for given $S∈R^{n×p}_p$}.<br/>Problem&nbsp;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&nbsp;&nbsp;Problem&nbsp;Ⅰ.<br/>The necessary and sufficient conditions for the solvability of&nbsp;Problem&nbsp;Ⅰ, the expression of the general solution of&nbsp;Problem&nbsp;Ⅰ and the solution of&nbsp;Problem&nbsp;Ⅱ are given for two case. For the general case, the equivalent form of conditions for the solvability of&nbsp;Problem&nbsp;&nbsp;Ⅰ is given.</p>},
issn = {1991-7139},
doi = {https://doi.org/1994-JCM-10229},
url = {https://global-sci.com/article/85845/the-solvability-conditions-for-the-inverse-problem-of-matrices-positive-semidefinite-on-a-subspace}
}