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In this paper we consider a class of regularized Gauss-Newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration. Such methods have the frozen feature that they require only the computation of the Fréchet derivative at the initial approximation. Thus the computational work is considerably reduced. Under certain mild conditions, we give the convergence analysis and derive various estimates, including the order optimality, on these methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to the class of inverse problems for coefficient identification with an adjoint problem approach related to nonlinear parabolic partial differential equations. The unknown coefficient depends on the gradient of the solution and belongs to a set of admissible coefficients. First, we present a coefficient-to-data mapping. Then, based on maximum principle and the adjoint problem of the direct problem, the integral identities will be obtained. Using these identities, we can show that the coefficient-to-data mapping is continuous and strictly monotone. Furthermore, an approximate solution to the inverse problem is constructed, and the error is analyzed. Finally, the applicability of the method is demonstrated in numerical examples. [Copyright &y& Elsevier]