کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1704961 | 1012420 | 2012 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Finite iterative algorithms for solving generalized coupled Sylvester systems-Part II: Two-sided and generalized coupled Sylvester matrix equations over reflexive solutions Finite iterative algorithms for solving generalized coupled Sylvester systems-Part II: Two-sided and generalized coupled Sylvester matrix equations over reflexive solutions](/preview/png/1704961.png)
In Part I of this article, we proposed a finite iterative algorithm for the one-sided and generalized coupled Sylvester matrix equations (AY − ZB, CY − ZD) = (E, F) and its optimal approximation problem over generalized reflexive matrices solutions. In Part II, an iterative algorithm is constructed to solve the two-sided and generalized coupled Sylvester matrix equations (AXB − CYD, EXF − GYH) = (M, N), which include Sylvester and Lyapunov matrix equations as special cases, over reflexive matrices X and Y. When the matrix equations are consistent, for any initial reflexive matrix pair [X1, Y1], the 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 reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation reflexive solution pair [X^,Y^] to a given matrix pair [X0, Y0] in Frobenius norm can be derived by finding the least-norm reflexive solution pair [X∼∗,Y∼∗] of a new corresponding generalized coupled Sylvester matrix equations (AX∼B-CY∼D,EX∼F-GY∼H)=(M∼,N∼), where M∼=M-AX0B+CY0D,N∼=N-EX0F+GY0H. Several numerical examples are given to show the effectiveness of the presented iterative algorithm.
Journal: Applied Mathematical Modelling - Volume 36, Issue 4, April 2012, Pages 1604–1614