On the construction of preconditioners by subspace decomposition

摘要

A preconditioner for the iterative solution of symmetric linear systems which arise in Galerkin's method is obtained by decomposition of the space into orthogonal subspaces. The preconditioner corresponds to a particular bilinear form and is actually a 2-level multigrid method. Applications are presented to the numerical solution of elliptic problems by the finite-element method and to the numerical solution of first-kind Fredholm integral equations by Tikhonov regularization.