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Abstract
In this paper, the possibility of using the reverse connection control for iteratively regularized Gauss–Newton-type algorithms is analyzed. It is shown that for the generalized Gauss–Newton iterations the diameter of the set containing the control elements can tend to ∞ as n → ∞. To further improve the stabilizing properties of the Gauss–Newton scheme, a new penalty term is proposed that can depend nonlinearly on the current iteration. As a test numerical example, a nonlinear inverse scattering problem of computing a 2D obstacle shape is considered.
Received: 2010-02-19
Published Online: 2010-05-31
Published in Print: 2010-May
© de Gruyter 2010
