A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the ...

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...

and Applied Analysis 3 to a class of complex matrix equations with conjugate and transpose of the unknowns. Jonsson and Kågström 24, 25 proposed recursive block algorithms for solving the coupled Sylvester matrix equations and the generalized Sylvester and Lyapunov Matrix equations. Very recently, Huang et al. 26 presented a finite iterative algorithms for the one-sided and generalized coupled ...

‎the global fom and gmres algorithms are among the effective‎ ‎methods to solve sylvester matrix equations‎. ‎in this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two cg-type algorithms for solving generalized sylvester matrix‎ ‎equations‎. ‎the proposed methods are iterative projection metho...

In various applications, for instance in the detection of a Hopf bifurcation or in solving separable boundary value problems using the two-parameter eigenvalue problem, one has to solve a generalized eigenvalue problem of the form (B1 ⊗A2 −A1 ⊗B2)z = μ(B1 ⊗ C2 − C1 ⊗B2)z, where matrices are 2 × 2 operator determinants. We present efficient methods that can be used to compute a small subset of t...

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...