1 Motivation This Master's Thesis project considers software for solving periodic Sylvester-type matrix equations. Recently, the ScaLAPACK-style library SCASY was completed. SCASY is a parallel HPC software library that solves for 42 sign and transpose variant of 8 common standard and generalized Sylvester-type matrix equations (see Table 1) which builds on the Table 1: The Sylvester-type matri...

This paper considers the solution to a class of the second-order Sylvester matrix equation EVF2 −AVF −CV = BW . Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the ...

‎The global generalized minimum residual (Gl-GMRES)‎ ‎method is examined for solving the generalized Sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {A_i } XB_i = C.]‎ ‎Some new theoretical results are elaborated for‎ ‎the proposed method by employing the Schur complement‎. ‎These results can be exploited to establish new convergence properties‎ ‎of the Gl-GMRES method for solving genera...

in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...

where X ∈ M(n,m)(K), play a central role in many areas of applied mathematics and in particular in systems and control theory. It is well known that if K is an algebraically closed field then the matrix equation (1) possesses a unique solution if and only if the matrices A and B have no common eigenvalues (see [[3]] and [11]). In this work we give a brief survey of methods used to solve the (SM...

For when the Sylvester matrix equation has a unique solution, this work provides a closed form solution, which is expressed as a polynomial of known matrices. In the case of non-uniqueness, the solution set of the Sylvester matrix equation is a subset of that of a deduced equation, which is a system of linear algebraic equations. c © 2005 Elsevier Ltd. All rights reserved.

The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood and there are stable and efficient numerical algorithms which solve these equations for smallto medium-sized matrices. However, develop...

The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood and there are stable and efficient numerical algorithms which solve these equations for smallto medium-sized matrices. However, develop...

We provide necessary and sufficient conditions for the generalized ⋆Sylvester matrix equation, AXB+CX ⋆ D = E, to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient matrices A,B,C,D (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the ex...

We provide necessary and sufficient conditions for the generalized ?Sylvester matrix equation, AXB +CX ? D = E, to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient matrices A,B,C,D (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the e...