On the convergence of two‐level Krylov methods for singular symmetric systems

We discuss the convergence of a two‐level version of the multilevel Krylov method for solving linear systems of equations with symmetric positive semidefinite matrix of coefficients. The analysis is based on the convergence result of Brown and Walker for the Generalized Minimal Residual method (GMRES), with the left‐ and right‐preconditioning implementation of the method. Numerical results based on diffusion problems are presented to show the convergence.