Abstract
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.
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