On a Modified Block Arnoldi Method for Solving Low-Rank Sylvester Equations

Krylov methods are widely used to solve large matrix equations. In this work, we are particularly interested in solving continuous and discrete low-rank Sylvester equations. In this context, we propose a modification of the block Arnoldi method so that the projection subspace contains in a limited way some additional blocks which are derived by multiplying the initial block by the inverse of one of the two coefficient matrices of the Sylvester equation. The efficiency of the suggested modified method, in comparison with the classical and extended block Arnoldi method, is confirmed with numerical examples.