Abstract
The generalized coupled Sylvester matrix equations ( AY - ZB , CY - ZD ) = ( E , F ) with unknown matrices Y , Z are encountered in many systems and control applications. Also these matrix equations have several applications relating to the problem of computing stable eigendecompositions of matrix pencils. In this work, we construct an iterative algorithm to solve the generalized coupled Sylvester matrix equations over reflexive matrices Y , Z . And when the matrix equations are consistent, for any initial matrix pair [ Y 0 , Z 0 ] , a reflexive solution pair can be obtained within finite iteration steps in the absence of roundoff errors, and the least Frobenius norm reflexive solution pair can be obtained by choosing a special kind of initial matrix pair. Also we obtain the optimal approximation reflexive solution pair to a given matrix pair [ Y ¯ , Z ¯ ] in the reflexive solution pair set of the generalized coupled Sylvester matrix equations ( AY - ZB , CY - ZD ) = ( E , F ) . Moreover, several numerical examples are given to show the efficiency of the presented iterative algorithm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.