A complete characterization of the convergence factor can be very useful when analyzing the asymptotic convergence of an iterative method. We will here establish a formula for the convergence factor of the method called residual inverse iteration, which is a method for nonlinear eigenvalue problems and a generalization of the well known inverse iteration. The formula for the convergence factor ...

We consider the Fourier analysis of multi-grid methods for symmetric positive definite and semi-positive definite linear systems arising from the discretizations of scalar PDEs. In this framework, the smoothing factor is frequently used to estimate the potential of a multigrid approach. In this paper, the smoothing factor is related to the actual two-grid convergence rate and also to the Vcycle...

We consider multigrid methods for symmetric positive definite linear systems. We present a new algebraic convergence analysis of two-grid schemes with inexact solution of the coarse grid system. This analysis allows us to bound the convergence factor of such perturbed two-grid schemes, assuming only a certain bound on the convergence factor for the unperturbed scheme (with exact solution of the...