Journal of Applied Mathematics

An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations

Feng Yin and Guang-Xin Huang

Full-text: Open access

Abstract

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations ( A X B - C Y D , E X F - G Y H ) = ( M , N ) , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y . When the matrix equations are consistent, for any initial generalized reflexive matrix pair [ X 1 , Y 1 ] , the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation generalized reflexive solution pair [ X ̂ , Y ̂ ] to a given matrix pair [ X 0 , Y 0 ] in Frobenius norm can be derived by finding the least-norm generalized reflexive solution pair [ X ̃ * , Y ̃ * ] of a new corresponding generalized coupled Sylvester matrix equation pair ( A X ̃ B - C Y ̃ D , E X ̃ F - G Y ̃ H ) = ( M ̃ , N ̃ ) , where M ̃ = M - A X 0 B + C Y 0 D , N ̃ = N - E X 0 F + G Y 0 H . Several numerical examples are given to show the effectiveness of the presented iterative algorithm.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 152805, 28 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495265

Digital Object Identifier
doi:10.1155/2012/152805

Mathematical Reviews number (MathSciNet)
MR2965698

Zentralblatt MATH identifier
1251.65063

Citation

Yin, Feng; Huang, Guang-Xin. An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations. J. Appl. Math. 2012 (2012), Article ID 152805, 28 pages. doi:10.1155/2012/152805. https://projecteuclid.org/euclid.jam/1355495265


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