  In this article we propose a novel nonstationary iterated Tikhonov (NIT) type
method for obtaining stable approximate solutions to ill-posed operator
equations modeled by linear operators acting between Hilbert spaces.
Geometrical properties of the problem are used to derive a new strategy for
choosing the sequence of regularization parameters (Lagrange multipliers) for
the NIT iteration. Convergence analysis for this new method is provided.
Numerical experiments are presented for two distinct applications: I) A 2D
elliptic parameter identification problem (Inverse Potential Problem); II) An
image deblurring problem. The results obtained validate the efficiency of our
method compared with standard implementations of the NIT method (where a
geometrical choice is typically used for the sequence of Lagrange multipliers).
