On a variable smoothing procedure for Krylov subspace methods

It is known that the convergence behavior of Galerkin-Krylov subspace methods for solving linear systems can be very erratic. A smoothing technique or a minimal residual seminorm variant of these Galerkin methods can be proposed to eliminate this problem. In this paper we examine a class of minimal residual seminorm methods, and show that this class of methods can be obtained from a variable smoothing technique applied to Galerkin methods.