Journal
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
Volume 46, Issue 3, Pages 488-502Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207721.2013.790999
Keywords
coupled Sylvester-conjugate matrix equations; Hermitian reflexive matrix; reflexive matrix; iterative algorithm
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It is known that solving coupled matrix equations with complex matrices can be very difficult and it is sufficiently complicated. In this work, we propose two iterative algorithms based on the Conjugate Gradient method (CG) for finding the reflexive and Hermitian reflexive solutions of the coupled Sylvester-conjugate matrix equations [GRAPHICS] (including Sylvester and Lyapunov matrix equations as special cases). The iterative algorithms can automatically judge the solvability of the matrix equations over the reflexive and Hermitian reflexive matrices, respectively. When the matrix equations are consistent over reflexive and Hermitian reflexive matrices, for any initial reflexive and Hermitian reflexive matrices, the iterative algorithms can obtain reflexive and Hermitian reflexive solutions within a finite number of iterations in the absence of roundoff errors, respectively. Finally, two numerical examples are presented to illustrate the proposed algorithms.
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