Krylov subspace methods for the generalized Sylvester equation

摘要

In the paper we propose Galerkin and minimal residual methods for iteratively solving generalized Sylvester equations of the form AXB − X = C. The algorithms use Krylov subspace for which orthogonal basis are generated by the Arnoldi process and reduce the storage space required by using the structure of the matrix. We give some convergence results and present numerical experiments for large problems to show that our methods are efficient.