The Inverse Problem for Part Symmetric Matrices on a Subspace

The Inverse Problem for Part Symmetric Matrices on a Subspace

Year:    2003

Author:    Zhen-Yun Peng, Xi-Yan Hu, Lei Zhang

Journal of Computational Mathematics, Vol. 21 (2003), Iss. 4 : pp. 505–512

Abstract

In this paper, the following two problems are considered:
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 $SR_{s,n}={A \in R^{n×n} | x^T(A-A^T)=0, \ {\rm for} \ {\rm all} \ x \in R(S)}$.

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.

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.


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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2003-JCM-10254

Journal of Computational Mathematics, Vol. 21 (2003), Iss. 4 : pp. 505–512

Published online:    2003-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Part symmetric matrix Inverse problem Optimal approximation.

Author Details

Zhen-Yun Peng

Xi-Yan Hu

Lei Zhang