Volume 22, Issue 5
Computing a Nearest P-Symmetric Nonnegative Definite Matrix Under Linear Restriction

Hua Dai

DOI:

J. Comp. Math., 22 (2004), pp. 671-680

Published online: 2004-10

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  • Abstract

Let P be an $n\times n$ symmetric orthogonal matrix. A real $n\times n$ matrix A is called P-symmetric nonnegative definite if A is symmetric nonnegative definite and $(PA)^T=PA. This paper is concerned with a kind of inverse problem for P-symmetric nonnegative definite matrices: Given a real $n\times n$ matrix $\widetidle{A}$, real $n\times m$ matrices X and B, find an $n\times n$ P-symmetric nonnegative definite matrix A minimizing $||A-\widetidle{A}||_F$ subject to AX =B. Necessary and sufficient conditions are presented for the solvability of the problem. The expression of the solution to the problem is given. These results are applied to solve an inverse eigenvalue problem for P-symmetric nonnegative definite matrices.

  • Keywords

Inverse problem Matrix approximation Inverse eigenvalue problem Symmet-ric nonnegative definite matrix

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@Article{JCM-22-671, author = {}, title = {Computing a Nearest P-Symmetric Nonnegative Definite Matrix Under Linear Restriction}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {5}, pages = {671--680}, abstract = { Let P be an $n\times n$ symmetric orthogonal matrix. A real $n\times n$ matrix A is called P-symmetric nonnegative definite if A is symmetric nonnegative definite and $(PA)^T=PA. This paper is concerned with a kind of inverse problem for P-symmetric nonnegative definite matrices: Given a real $n\times n$ matrix $\widetidle{A}$, real $n\times m$ matrices X and B, find an $n\times n$ P-symmetric nonnegative definite matrix A minimizing $||A-\widetidle{A}||_F$ subject to AX =B. Necessary and sufficient conditions are presented for the solvability of the problem. The expression of the solution to the problem is given. These results are applied to solve an inverse eigenvalue problem for P-symmetric nonnegative definite matrices. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10295.html} }
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