EXTENDED BLOCK HESSENBERG METHOD FOR LARGE-SCALE SYLVESTER DIFFERENTIAL MATRIX EQUATIONS.

In this paper, we consider large-scale low-rank Sylvester differential matrix equations. We present two iterative methods for the approximate solution of such difierential matrix equations. The first approach is based on the integral expression of the exact solution which exploits an extended block Krylov subspace method to compute the exponential of a matrix times a block of vectors. In the second method, we first project the initial value problem onto an extended block Krylov subspace and acquire a low-dimensional Sylvester difierential matrix equation with a low-rank constant term. Then the reduced Sylvester difierential matrix equation is solved by the backward difierentiation formula method (BDF) and the derived solution is used to construct the low-rank approximate solutions of the original initial value problem. The iterative approaches are followed until some certain accuracy is obtained. We give some theoretical results and some numerical examples to show the eficiency of the proposed methods. [ABSTRACT FROM AUTHOR]