Abstract and Applied Analysis

Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized ( P , Q ) -Reflexive Matrices

Ning Li and Qing-Wen Wang

Full-text: Open access

Abstract

The matrix equation l = 1 u A l X B l + s = 1 v C s X T D s = F , which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation l = 1 u A l X B l + s = 1 v C s X T D s = F over generalized ( P , Q ) -reflexive matrices. The proposed iterative algorithm automatically determines the solvability of the quaternion matrix equation over generalized ( P , Q ) -reflexive matrices. When the matrix equation is consistent over generalized ( P , Q ) -reflexive matrices, the sequence { X ( k ) } generated by the introduced algorithm converges to a generalized ( P , Q ) -reflexive solution of the quaternion matrix equation. And the sequence { X ( k ) } converges to the least Frobenius norm generalized ( P , Q ) -reflexive solution of the quaternion matrix equation when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate generalized ( P , Q ) -reflexive solution for a given generalized ( P , Q ) -reflexive matrix X 0 can be derived. The numerical results indicate that the iterative algorithm is quite efficient.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 831656, 15 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512084

Digital Object Identifier
doi:10.1155/2013/831656

Mathematical Reviews number (MathSciNet)
MR3121402

Citation

Li, Ning; Wang, Qing-Wen. Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized $\left(P,Q\right)$ -Reflexive Matrices. Abstr. Appl. Anal. 2013 (2013), Article ID 831656, 15 pages. doi:10.1155/2013/831656. https://projecteuclid.org/euclid.aaa/1393512084


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