Hassan Jamali - Department of Mathematics‎, ‎Faculty of Mathematics and computer Sciences‎, ‎Vali-e-Asr‎ ‎University of Rasanjan‎, ‎Rafsanjan‎, ‎Iran‎.
Mohsen Kolahdouz - Department of Mathematics‎, ‎Faculty of Mathematics and computer Sciences‎, ‎Vali-e-Asr‎ ‎University of Rasanjan‎, ‎Rafsanjan‎, ‎Iran‎.

‎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.

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