An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices and . When the matrix equations are consistent, for any initial generalized reflexive matrix pair , 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 to a given matrix pair in Frobenius norm can be derived by finding the least-norm generalized reflexive solution pair of a new corresponding generalized coupled Sylvester matrix equation pair , where . Several numerical examples are given to show the effectiveness of the presented iterative algorithm.
Feng Yin. Guang-Xin Huang. "An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations." J. Appl. Math. 2012 1 - 28, 2012. https://doi.org/10.1155/2012/152805