Algebraic study of multigrid methods for symmetric, definite problems

摘要

We present a convergence theory based on a simple algebraic assumption, which permits us to analyze multilevel iterative methods for symmetric, positive definite linear systems. Coarse grid problems are derived variationally. We prove fast convergence of V- and W-cycles with any positive number of smoothing steps under a discrete analogue of the H2 and H1+\Ga regularity assumption, respectively, and for a wide class of smoothings including arbitrarily ordered Gauss-Seidel and steepest descent.