We consider the uniqueness of solution (nonsingularity) of systems of r generalized Sylvester and ⋆-Sylvester equations with n × n coefficient matrices. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ⋆-Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix penc...

in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

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.

In this article, we study methods to solve a Sylvester equation in the form of $\mathbf {A}\mathbf {X}+\mathbf {X}\mathbf {B}=\mathbf {C}$ for given matrices {A}, \mathbf {B}, {C}\in \mathbb {R}^{n\times n}$ ...

Recently, recursive blocked algorithms for solving triangular one-sided and two-sided Sylvester-type equations were introduced by Jonsson and K̊agström. This elegant yet simple technique enables an automatic variable blocking that has the potential of matching the memory hierarchies of today’s HPC systems. The main parts of the computations are performed as level 3 general matrix multiply and ad...

We propose a displacement structure based rank-revealing algorithm for Sylvester matrix, then apply it to compute approximate greatest common division of two univariate polynomials with floating-point coefficients. This structured rank-revealing method is based on a stabilized version of the generalized Schur algorithm [8], and is a fast rank-revealing method in the sense that, all computations...