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

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

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