Year: 2002
Author: Dong-Xiu Xie, Xi-Yan Hu, Lei Zhang
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 3 : pp. 245–256
Abstract
This paper is mainly concerned with solving the following two problems:
Problem I. Given $X$ $\in$ $ C^{n \times m} $, $\Lambda = {\rm diag}( \lambda_1, \lambda_2, \dots, \lambda_m) \in C^{m\times m}$. Find $ A \in ABSR^{n \times n} $ such that $$AX=X\Lambda$$where $ABSR^{n \times n}$ is the set of all real $n\times n$ anti-bisymmetric matrices.
Problem Ⅱ. Given $A^* \in R^{n \times n}$. Find $\hat{A} \in S_E $ such that $$||A^* - \hat{A}||_F=\underset{A\in S_E}{\min}||A^*- A ||_F,$$where $||\cdot||_F$ is Frobenius norm, and $S_E$ denotes the solution set of Problem Ⅰ.
The necessary and sufficient conditions for the solvability of Problem Ⅰ have been studied. The general form of $ S_E $ has been given. For Problem Ⅱ the expression of the solution has been provided.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2002-JCM-8914
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 3 : pp. 245–256
Published online: 2002-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Eigenvalue problem Norm Approximate solution.