Convergence analysis of simplified iteratively regularized Gauss–Newton method in a Banach space setting. Issue 15 (18th November 2018) - Mahale, Pallavi; Dixit, Sharad Kumar
Abstract: 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, where 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 of the solution 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 .