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

Range-relaxed criteria for choosing the Lagrange multipliers in nonstationary iterated Tikhonov method