Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 20, Number 4 (2013), 639-653.
The reflexive and Hermitian reflexive solutions of the generalized Sylvester-conjugate matrix equation
Masoud Hajarian and Mehdi Dehghan
Abstract
The main purpose of this correspondence is to establish two gradient based iterative (GI) methods extending the Jacobi and Gauss-Seidel iterations for solving the generalized Sylvester-conjugate matrix equation \begin{equation*} A_1XB_1+A_2\overline{X}B_2+C_1YD_1+C_2\overline{Y}D_2=E, \end{equation*} over reflexive and Hermitian reflexive matrices. It is shown that the iterative methods, respectively, converge to the reflexive and Hermitian reflexive solutions for any initial reflexive and Hermitian reflexive matrices. We report numerical tests to show the effectiveness of the proposed approaches.
Article information
Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 4 (2013), 639-653.
Dates
First available in Project Euclid: 22 October 2013
Permanent link to this document
https://projecteuclid.org/euclid.bbms/1382448185
Digital Object Identifier
doi:10.36045/bbms/1382448185
Mathematical Reviews number (MathSciNet)
MR3129064
Zentralblatt MATH identifier
1282.15014
Subjects
Primary: 15A24: Matrix equations and identities 65F10: Iterative methods for linear systems [See also 65N22] 65F30: Other matrix algorithms
Keywords
The generalized Sylvester-conjugate matrix
equations Reflexive solution pair Hermitian reflexive solution pair Iterative method
Citation
Hajarian, Masoud; Dehghan, Mehdi. The reflexive and Hermitian reflexive solutions of the generalized Sylvester-conjugate matrix equation. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 4, 639--653. doi:10.36045/bbms/1382448185. https://projecteuclid.org/euclid.bbms/1382448185
