Abstract:
We propose and study an iterative method for finding quasisolutions
of nonlinear ill-posed operator equations on closed convex subsets of
a Hilbert space in the presence of errors. The process under
consideration combines the gradient-projection method and the
projections of iterations obtained onto suitably constructed
finite-dimensional subspaces. We establish that the iterations
generated by our method are stabilized in a small neighborhood of the
quasisolution as the iteration number increases.