Computation of Sylvester and Stein matrix equations' solutions by Iterative Decreasing Dimension Method

Authors : Oğuzer Sinan

Pages : 486-491

View : 15 | Download : 7

Publication Date : 2019-10-15

Article Type : Research

Abstract :Sylvester matrix equation  and the  Stein matrix equation which have very important applications in the stability analysis of continuous-time and discrete-time linear systems, respectively are studied. The solutions of these equations  be possible  demonstrated by  a number of methods. Been one of them transformation  to the  system of linear equation  was examined. Algorithms that provide transformation to $Ax=f$ system of linear equation was introduced. Iterative Decreasing Dimension  Method ($IDDM$) algorithm was applicated for the solution of the obtained system. The $IDDM$ algorithm has been evaluated according to the Gaussian elimination type algorithms. The $IDDM$ algorithm is evade from  divisor of zero based on its algorithmic structure. Depending on the study, codes for calculation were prepared in the MAPLE program code development environment.
Keywords : Sylvester matrix equation, Stein matrix equation, IDDM, Kronecker product