We present a new minimal residual method, called global R-linear GMRES, to solve the R-linear matrix equations X + AXB = C and X + AXB = C, where C, X ∈ Cm×n, X denotes the complex conjugate of X, X its complex conjugate transpose, and A, B are complex matrices with appropriate dimensions. We show that the new method requires fewer matrix-matrix products than the global GMRES method applied to ...

In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where A ∈ Rn×n, B ∈ Rs×s, X and C ∈ Rn×s. These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-SylvesterLike(GFSL) and Global GMRES-Sylvester-Like(GGSL) algorithms, respectively. Some theoretical results and ...

Working with input-output transfer functions in the frequency domain and exploiting a formulation involving generalized Sylvester resultants, we are able to derive necessary and sufficient conditions for generic invariant factor assignment, in several cases, using proper dynamic output feedback compensators.

This paper presents a new version of the successive approximationsmethod for solving Sylvester equationsAX XB = C, where A and B are symmetric negative and positive definite matrices, respectively. This method is based on the block GMRES-Sylvester method. We also discuss the convergence of the new method. Some numerical experiments for obtaining the numerical solution of Sylvester equations are...

This paper presents equivalent forms of the Sylvester matrix equations. These equivalent forms allow us to use block linear methods for solving large Sylvester matrix equations. In each step of theses iterative methods we use global FOM or global GMRES algorithm for solving an auxiliary block matrix equations. Also, some numerical experiments for obtaining the numerical approximated solution of...

In this paper, we propose a new method to design an observer and control the linear singular systems described by Chebyshev wavelets. The idea of the proposed approach is based on solving the generalized Sylvester equations. An example is also given to illustrate the procedure.