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.