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...

This paper presents preconditioned Galerkin and minimal residual algorithms for the solution of Sylvester equations AX XB = C. Given two good preconditioner matricesM and N for matrices A and B, respectively, we solve the Sylvester equations MAXN MXBN =MCN. The algorithms use the Arnoldi process to generate orthonormal bases of certain Krylov subspaces and simultaneously reduce the order of Syl...

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary sufficient solvability conditions for a system Sylvester-type quaternion matrix equations, give an expression general solution to when it is solvable. As application system, consider special symmetry solution, named η-Hermitian equations. Moreover, present algorithm numerical example verif...

Fixed-order controller design for LTI-SISO polytopic systems is investigated using rank deficiency constraint on the controller Sylvester resultant matrix. It is shown that the non-convexity of fixed-order controller design problem can be contracted in a rank deficiency constraint on Sylvester resultant matrix of the controller. Then, an improved convex approximation of the rank deficiency cons...

We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...

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...

Descriptor systems consisting of a large number of differential-algebraic equations (DAEs) usually arise from the discretization of partial differential-algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear DAEs to ordinary differential equations. A significant computational advantage is obtained b...

We investigate the factored ADI iteration for large and sparse Sylvester equations. A novel low-rank expression for the associated Sylvester residual is established which enables cheap computations of the residual norm along the iteration, and which yields a reformulated factored ADI iteration. The application to generalized Sylvester equations is considered as well. We also discuss the efficie...

‎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...