Volume 15, Issue 1
Least-squares solutions of the equation AX=B over anti-Hermitian generalized Hamiltonian matrices
DOI:

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 15 (2006), pp. 60-66

Published online: 2006-02

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• Abstract

A real $n\times n$ symmetric matrix $X=(x_{ij})_{n \times n}$ is called a bisymmetric matrix if $x_{ij}=x_{n+1-j, n+1-i}$. Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation $A^{T}XA=B$ over bisymmetric matrices is proposed. The expression of the least-squares solutions is given. Moreover, in the corresponding solution set, the optimal approximate solution to a given matrix is also derived. A numerical algorithm for finding the optimal approximate solution is also described.

• Keywords

@Article{NM-15-60, author = {Z. Zhang and C. Liu}, title = {Least-squares solutions of the equation AX=B over anti-Hermitian generalized Hamiltonian matrices}, journal = {Numerical Mathematics, a Journal of Chinese Uniersities}, year = {2006}, volume = {15}, number = {1}, pages = {60--66}, abstract = { A real $n\times n$ symmetric matrix $X=(x_{ij})_{n \times n}$ is called a bisymmetric matrix if $x_{ij}=x_{n+1-j, n+1-i}$. Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation $A^{T}XA=B$ over bisymmetric matrices is proposed. The expression of the least-squares solutions is given. Moreover, in the corresponding solution set, the optimal approximate solution to a given matrix is also derived. A numerical algorithm for finding the optimal approximate solution is also described.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/10085.html} }