Some iterative methods for solving operator equations by using fusion frames

Abstract

‎In this paper‎, ‎two iterative methods are constructed to solve the operator equation $ Lu=f $ where $ L:H\rightarrow H $ is a bounded‎, ‎invertible and self-adjoint linear operator on a separable Hilbert space $ H $‎. ‎By using the concept of fusion frames‎, ‎which is a generalization of frame theory‎, ‎we design some algorithms based on Chebyshev polynomials and adaptive one according to conjugate gradient iterative method‎, ‎and accordingly‎, ‎we then investigate their convergence via their correspond convergence rates‎.