  In this paper, we propose and analyze a fast two-point gradient algorithm for
solving nonlinear ill-posed problems, which is based on the sequential subspace
optimization method. A complete convergence analysis is provided under the
classical assumptions for iterative regularization methods. The design of the
two-point gradient method involves the choices of the combination parameters
which is systematically discussed. Furthermore, detailed numerical simulations
are presented for inverse potential problem, which exhibit that the proposed
method leads to a strongly decrease of the iteration numbers and the overall
computational time can be significantly reduced.
