Superlinear Convergence of Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space

The conjugate gradient and minimum residual methods for self-adjoint problems in Hilbert space are considered. Linear and superlinear convergence results with respect to both Q- and R-rates are reviewed. New results on l-step Q-superlinear and R-superlinear convergence for the minimum residual method are provided, and examples are considered to underscore the relevance of a Hilbert space theory.