Some complex quaternionic equations in the type AX - XB = C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.

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...

This Licentiate Thesis contains contributions in two different subfields of Computing Science: parallel ScaLAPACK-style algorithms for Sylvester-type matrix equations and periodic eigenvalue reordering in a cyclic product of matrices. Sylvester-type matrix equations, like the continuous-time Sylvester equation AX −XB = C, where A of size m×m, B of size n×n and C of size m×n are general matrices...

‎In this paper‎, ‎an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed‎. ‎The convergence analysis of the algorithm is investigated‎. ‎We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions‎. ‎Finally‎, ‎some numerical examples are given to demons...

LOW-RANK SOLUTION METHODS FOR LARGE-SCALE LINEAR MATRIX EQUATIONS Stephen D. Shank DOCTOR OF PHILOSOPHY Temple University, May, 2014 Professor Daniel B. Szyld, Chair We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational Krylov subspaces to solve equations w...

‎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...

An efficient computational method is presented for state space analysis of singular systems via Haar wavelets. Singular systems are those in which dynamics are governed by a combination of algebraic and differential equations. The corresponding differential-algebraic matrix equation is converted to a generalized Sylvester matrix equation by using Haar wavelet basis. First, an explicit expressio...

We consider the solution of the ?-Sylvester equation AX±X?B? = C, for ? = T,H and A,B,∈ Cm×n, and some related linear matrix equations (AXB? ± X? = C, AXB? ± CX?D? = E, AX ± X?A? = C, AX ± Y B = C, AXB ± CY D = E, AXA? ± BY B? = C and AXB ± (AXB)? = C). Solvability conditions and stable numerical methods are considered, in terms of the (generalized and periodic) Schur, QR and (generalized) sing...