A New Method for the Bisymmetric Minimum Norm Solution of the Consistent Matrix EquationsA1XB1=C1,A2XB2=C2

Aijing Liu,Guoliang Chen,Xiangyun Zhang

doi:10.1155/2013/125687

Aijing Liu, Guoliang Chen + Show 1 more

Open Access

https://doi.org/10.1155/2013/125687

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Abstract

We propose a new iterative method to find the bisymmetric minimum norm solution of a pair of consistent matrix equationsA1XB1=C1,A2XB2=C2. The algorithm can obtain the bisymmetric solution with minimum Frobenius norm in finite iteration steps in the absence of round-off errors. Our algorithm is faster and more stable than Algorithm 2.1 by Cai et al. (2010).

Highlights

Let Rm×n denote the set of m × n real matrices
Cai et al [10, 11] proposed iterative methods to solve the bisymmetric solutions of the matrix equations A1XB1 = C1, A2XB2 = C2
We propose a new iterative algorithm to solve the bisymmetric solution with the minimum Frobenius norm of the consistent matrix equations A1XB1 = C1, A2XB2 = C2, which is faster and more stable than Cai’s algorithm (Algorithm 2.1) in [10]

Summary

Introduction

Let Rm×n denote the set of m × n real matrices. Let BSRn×n denote n × n real bisymmetric matrices. Peng et al [9] presented an iterative method to obtain the least squares reflexive solutions of the matrix equations A1XB1 = C1, A2XB2 = C2. Cai et al [10, 11] proposed iterative methods to solve the bisymmetric solutions of the matrix equations A1XB1 = C1, A2XB2 = C2. We propose a new iterative algorithm to solve the bisymmetric solution with the minimum Frobenius norm of the consistent matrix equations A1XB1 = C1, A2XB2 = C2, which is faster and more stable than Cai’s algorithm (Algorithm 2.1) in [10].

A New Iterative Algorithm

Numerical Examples