Convergence analysis of simplified iteratively regularized Gauss-Newton method in a Banach space setting

摘要

Iteratively regularized Gauss-Newton method considered by Qinian Jin and Min Zhong (2013), where the iterates are defined by convex optimization problem to get the approximate solution of nonlinear ill-posed equation of the form F(x) = y, where F : D(F) subset of X - Y is an operator between Banach spaces X and Y, involves calculation of the derivatives of F at each iterate. In this paper, we suggest a modified form of the iteratively regularized Gauss-Newton method in Banach spaces which requires the derivative of F only at an initial approximation x(0) of the solution x(+). We study convergence analysis of the method under the same a-posteriori rules as considered by Qinian Jin and Min Zhong (2013). The error estimates for this method are obtained under a modified source condition which also involves the derivative of F only at x(0).