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

Hua Dai

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 $\widetilde{A}$, real $n\times m$ matrices $X$ and $B$, find an $n\times n$ P-symmetric nonnegative definite matrix $A$ minimizing $||A-\widetilde{A}||_F$ 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, Symmetric nonnegative definite matrix.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-671, author = {Hua Dai}, 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 $\widetilde{A}$, real $n\times m$ matrices $X$ and $B$, find an $n\times n$ P-symmetric nonnegative definite matrix $A$ minimizing $||A-\widetilde{A}||_F$ 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} }
TY - JOUR T1 - Computing a Nearest P-Symmetric Nonnegative Definite Matrix Under Linear Restriction AU - Hua Dai JO - Journal of Computational Mathematics VL - 5 SP - 671 EP - 680 PY - 2004 DA - 2004/10 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10295.html KW - Inverse problem, Matrix approximation, Inverse eigenvalue problem, Symmetric nonnegative definite matrix. AB -

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 $\widetilde{A}$, real $n\times m$ matrices $X$ and $B$, find an $n\times n$ P-symmetric nonnegative definite matrix $A$ minimizing $||A-\widetilde{A}||_F$ 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.

Hua Dai. (2004). Computing a Nearest P-Symmetric Nonnegative Definite Matrix Under Linear Restriction. Journal of Computational Mathematics. 22 (5). 671-680. doi:
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