The solution of large scale Sylvester matrix equation plays an important role in control and large scientific computations. A popular approach is to use the global GMRES algorithm. In this work, we first consider the global GMRES algorithm with weighting strategy, and propose some new schemes based on residual to update the weighting matrix. Due to the growth of memory requirements and computat...

In this paper, by extending the well-known Jacobi and Gauss–Seidel iterations for Ax = b, we study iterative solutions of matrix equations AXB = F and generalized Sylvester matrix equations AXB + CXD = F (including the Sylvester equation AX + XB = F as a special case), and present a gradient based and a least-squares based iterative algorithms for the solution. It is proved that the iterative s...

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy. Keywords—Pro...

Combination of real and imaginary parts (CRI) works well for solving complex symmetric linear systems. This paper develops a generalization CRI method to determine the solution Sylvester matrix equation. We show that this, regardless condition, converges At end we test new scheme by numerical example.

The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation AX +XB = C where A = (aij) ∈ Rn×n , B = (bij) ∈ Rm×m are crisp Mmatrices, C = (cij) ∈ Rn×m is fuzzy matrix and X ∈ Rn×m is unknown,by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system to an (mn)×(mn) fuzzy system of linear equatio...

In this paper, we consider the fuzzy Sylvester matrix equation AX + XB = C, where A ∈ Rn×n and B ∈ Rm×m are crisp M-matrices, C is an n×m fuzzy matrix and X is unknown. We first transform this system to an (mn)× (mn) fuzzy system of linear equations. Then we investigate the existence and uniqueness of a fuzzy solution to this system. We use the accelerated overrelaxation method to compute an ap...

We present a direct algorithm for computing an orthogonal similarity transformation which interchanges neighboring diagonal blocks in a matrix in real Schur form. The algorithm does not require the solution of the associated Sylvester equation. Numerical tests suggest the backward stability of the scheme.