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Journal of Shanghai University >

2011 , Vol. 17 >Issue 3: 263 - 265

DOI: https://doi.org/doi:10.3969/j.issn.1007-2861.2011.03.009

Mathematics.Physics and Chemistry

Centrosymmetric Tridiagonal Least Square Solution to Matrix Equation

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  • 1. College of Sciences, Shanghai University, Shanghai 200444, China;
    2. Department of Mathematics, Zunyi Normal College, Zunyi 563000, Guizhou, China

Online published: 2011-06-24

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Abstract

The matrix equation 〖WTHX〗AX〖WTBX〗=〖WTHX〗B〖WTBZ〗 is considered, and a necessary and sufficient condition for the existence of centrosymmetric tridiagonal solutions is given. A new result of the following problem is obtained which related to the leastsquares solutions of 〖WTHX〗AX〖WTBX〗=〖WTHX〗B〖WTBZ〗 for 〖WTHX〗X〖WTBZ〗: given 〖WTHX〗A, B〖WTBZ〗∈〖WTHX〗R〖WTBX〗m×n,〖WTBZ〗 find a centrosymmetric tridiagonal matrix 〖WTHX〗X〖WTBZ〗∈〖WTHX〗R〖WTBX〗m×n〖WTBZ〗 such that ‖〖WTHX〗AX〖WTBZ〗-〖WTHX〗B〖WTBZ〗‖ is minimal.

Key words：  matrix equation; centrosymmetric tridiagonal matrix; leastsquares solution

Cite this article

ZHANG Xiang, WANG Qing-Wen . Centrosymmetric Tridiagonal Least Square Solution to Matrix Equation[J]. Journal of Shanghai University, 2011 , 17(3) : 263 -265 . DOI: doi:10.3969/j.issn.1007-2861.2011.03.009

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