Paper Info
Title
An iterative algorithm for the least squares bisymmetric solutions of the matrix equations A1XB1=C1,A2XB2=C2
Abstract
In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min@?(A"1XB"1A"2XB"2)-(C"1C"2)@? over bisymmetric matrices. By this algorithm, for any initial bisymmetric matrix X"0, a solution X^* can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation solution X@^ to a given matrix X@? in the Frobenius norm can be derived by finding the least norm bisymmetric solution of a new corresponding minimum Frobenius norm problem. Given numerical examples show that the iterative algorithm is quite effective in actual computation.
Year
DOI
Venue
2009
10.1016/j.mcm.2009.07.004
Mathematical and Computer Modelling
Keywords
DocType
Volume
minimum frobenius norm,matrix equation,norm bisymmetric solution,initial bisymmetric matrix x,least squares bisymmetric solution,solution x,unique optimal approximation solution,bisymmetric matrix,squares bisymmetric solution,iterative algorithm,optimal approximation solution,matrix x,frobenius norm,corresponding minimum frobenius norm
Journal
50
Issue
ISSN
Citations 
7-8
Mathematical and Computer Modelling
4
PageRank 
References 
Authors
0.44
2
2
Name
Order
Citations
PageRank
Jing Cai140.44
Guo-Liang Chen210617.84