On the iterative
bisymmetric solution of
general coupled matrix equations
∗
Dongping Li
a†
, Shu-Xin Miao
a,b,
, Bing Zheng
a
a
School of Mathematics and Statistics, Lanzhou University,
Lanzhou 730000, P.R. China
b
College of Mathematics and Information Science, North-West Normal University,
Lanzhou 730070, P.R. China
Abstract. A matrix A = (a
i,j
) ∈ R
n×n
is called bisymmetric matrix if a
i,j
= a
j,i
=
a
n+1−j,n+1−i
holds for all 1 ≤ i, j ≤ n. In this paper, an efficient algorithm is presented
to find the bisymmetric solution of the general coupled matrix equations. When the
general coupled matrix equations is consistent on bisymmetric solutions, then for any
initial bisymmetric matrix group, a group of bisymmetric solution can be obtained
within finite iterative steps in the absence of round off errors, and the least norm
bisymmetric solution can be obtained by cho osing a group of special kind of initial
matrices. Finally, we test the algorithm and show it’s effectiveness by a numerical
example.
Keywords: The general coupled matrix equations; Least norm solution; Bisym-
metric solution.
AMS subject classifications: 15A18, 65F10
1 Introduction
Throughout this paper, we denote by R
m×n
, SR
n×n
and BSR
n×n
the set of m × n real
matrices, n × n real symmetric matrices and n × n real bisymmetric matrices, respectively.
We use A
T
to denote the transpose of matrix A. S
n
(S
n
= (e
n
, e
n−1
, . . . , e
1
)) refers to the
∗
Supp orted by the start-up fund of Lanzhou University and the Natural Science Foundation of Gansu
Province (3ZS051-A25-020), P.R. China.
†
Corresp onding author. E-mail address: lidping06@lzu.cn(D.-P. Li).
1
http://www.paper.edu.cn
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