using frames of subspaces in galerkin and richardson methods for solving operator equations

In this paper, two iterative methods are constructed to solve the operator equation lu = f where l : h →h is a bounded, invertible and self- adjoint linear operator on a separable hilbert space h. by using the concept of frames of subspaces, which is a generalization of frame theory, we design some algorithms based on galerkin and richardson methods, and then we investigate the convergence and optimality of them.