A sharp convergence estimate for the method of subspace corrections for singular systems of equations

Abstract

This paper is devoted to the convergence rate estimate for the method of <italic>successive</italic> subspace corrections applied to symmetric and positive semidefinite ( <italic>singular</italic> ) problems. In a general Hilbert space setting, a convergence rate identity is obtained for the method of subspace corrections in terms of the subspace solvers. As an illustration, the new abstract theory is used to show uniform convergence of a multigrid method applied to the solution of the Laplace equation with pure Neumann boundary conditions.