- Konuralp Journal of Mathematics
- Vol: 7 Issue: 2
- Computation of Sylvester and Stein matrix equations' solutions by Iterative Decreasing Dimension Met...
Computation of Sylvester and Stein matrix equations' solutions by Iterative Decreasing Dimension Method
Authors : Oğuzer Sinan
Pages : 486-491
View : 11 | Download : 4
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