An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations
نویسندگان
چکیده
An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations AXB − CYD,EXF − GYH 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 X1, Y1 , 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 X0, Y0 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 ̃ XB − C ̃ YD,E ̃ XF −G ̃ YH ̃ M, ̃ N , where
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ورودعنوان ژورنال:
- J. Applied Mathematics
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012