On the construction of preconditioners by subspace decomposition

AbstractA 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