Application of a Kind of Krylov Subspace Methods in Solving the Sylvester Equation

Block Krylov subspace methods for solving the Sylvester matrix equationAX+XB=EFT is proposed.When both matrices A and B are large and the right-hand side matrix is of small rank,it is shown that how to extract low-rank approximations.Some theoretical results are given and numerical experiments show the effectiveness of these block methods.