Bulletin of the Belgian Mathematical Society - Simon Stevin

The reflexive and Hermitian reflexive solutions of the generalized Sylvester-conjugate matrix equation

Masoud Hajarian and Mehdi Dehghan

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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


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