The Reflexive Optimal Approximation Solution of Matrix Equation AXB + CYD = E

Author

Sun, Heming ; Ye, Tingting ; Yang, Jiawen

Author_Institution

Coll. of Sci., Hohai Univ. Nanjing, Nanjing, China

fYear

2012

fDate

23-26 June 2012

Firstpage

36

Lastpage

40

Abstract

This paper investigates the matrix nearness problem associated with the matrix equation AXB+XYD=E over reflexive (anti-reflexive) matrices. The problem is a 3-step optimization problem. Firstly, the matrices X and Y were defined as reflexive (anti-reflexive) matrices. Then the Frobenius norm of AXB+CYD-E was minimized. Lastly, the nearest matrices to the given matrices X* and Y* among the solutions of second step were determined. By making use of the orthonormal basis of a matrix null space, we obtained the representation of the optimal approximation solution of the above problem. The effectiveness of the representation is verified by numerical examples.

Keywords

approximation theory; matrix algebra; matrix equation; matrix nearness problem; matrix null space; optimal approximation solution; reflexive matrices; reflexive optimal approximation solution; Approximation algorithms; Educational institutions; Equations; Least squares approximation; Null space; Symmetric matrices; Kronecker product; Sylvester matrix equation; optimal approximation; orthonormal basis; reflexive matrix;

fLanguage

English

Publisher

ieee

Conference_Titel

Computational Sciences and Optimization (CSO), 2012 Fifth International Joint Conference on

Conference_Location

Harbin

Print_ISBN

978-1-4673-1365-0

Type

conf

DOI

10.1109/CSO.2012.16

Filename

6274673