FD-Method: the Exponential Rate of Convergence

In this article, we describe a functional–discrete method (FD>-method) for solving operator equations and abstract eigenvalue problems. The algorithm of the method includes a recurrent solution of a sequence of problems with a fixed operator, which is simpler than the initial one, and a changing right-hand side. We prove that, with fairly general assumptions, the FD-method converges with the rate of a geometric progression, i.e., has exponential convergence rate.