Application of frames in Chebyshev and conjugate gradient methods

‎Given a frame of a separable Hilbert space H‎, ‎we present some‎ ‎iterative methods for solving an operator equation Lu=f, ‎where L is a bounded‎, ‎invertible and symmetric‎ ‎operator on H‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we investigate the‎ ‎convergence and optimality of them.