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:Hrightarrow 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.

Keywords:

‎Hilbert spaces , Operator equation , Frame , Frames of subspaces , Richardson method , Galerkin method