## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014 (2014), Article ID 352327, 9 pages.

### Generalized Reflexive and Generalized Antireflexive Solutions to a System of Matrix Equations

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#### Abstract

Two efficient iterative algorithms are presented to solve a system of matrix equations ${A}_{1}{X}_{1}{B}_{1}$ + ${A}_{2}{X}_{2}{B}_{2}$ $=E$, ${C}_{1}{X}_{1}{D}_{1}$ + ${C}_{2}{X}_{2}{D}_{2}$ $=F$ over generalized reflexive and generalized antireflexive matrices. By the algorithms, the least norm generalized reflexive (antireflexive) solutions and the unique optimal approximation generalized reflexive (antireflexive) solutions to the system can be obtained, too. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. The given numerical examples demonstrate that the iterative algorithms are efficient.

#### Article information

**Source**

J. Appl. Math., Volume 2014 (2014), Article ID 352327, 9 pages.

**Dates**

First available in Project Euclid: 2 March 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1425305544

**Digital Object Identifier**

doi:10.1155/2014/352327

**Mathematical Reviews number (MathSciNet)**

MR3176816

**Zentralblatt MATH identifier**

07010609

#### Citation

Lin, Yong; Wang, Qing-Wen. Generalized Reflexive and Generalized Antireflexive Solutions to a System of Matrix Equations. J. Appl. Math. 2014 (2014), Article ID 352327, 9 pages. doi:10.1155/2014/352327. https://projecteuclid.org/euclid.jam/1425305544

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