Abstract: In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.
Abstract: 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.