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The use of second order information on the forward operator often comes at avery moderate additional computational price in the context of parameteridentification probems for differential equation models. On the other hand theuse of general (non-Hilbert) Banach spaces has recently found much interest dueto its usefulness in many applications. This motivates us to extend the secondorder method previously considered by the author in a Hilbert space setting,(see also Hettlich and Rundell 2000) to a Banach space setting and analyze itsconvergence. We here show rates results for a particular source condition anddifferent exponents in the formulation of Tikhonov regularization in each step.This includes a complementary result on the (first order) iterativelyregularized Gauss-Newton method (IRGNM) in case of a one-homogeneous datamisfit term, which corresponds to exact penalization. The results clearly showthe possible advantages of using second order information, which get mostpronounced in this exact penalization case. Numerical simulations for acoefficient identification problem in an elliptic PDE illustrate thetheoretical findings.

A convergence rates result for an iteratively regularized Gauss-Newton-Halley method in Banach space