Some approximated solutions for operator equations by using frames

In this paper we give some approximated solutions for an operator equation lu=f where l:H?H is a bounded and self adjoint operator on a separable Hilbert space H. We use frames in order to precondition the linear equation so that convergence of iterative methods is improved. Also we find an exact solution associated to a frame and then we seek an approximated solution in a finite dimensional subspace of H that is generated by a finite frame sequence.