Convergence analysis of simplified iteratively regularized Gauss–Newton method in a Banach space setting. Issue 15 (18th November 2018)

• Record Type: Journal Article
• Authors: Mahale, Pallavi; Dixit, Sharad Kumar
• Is Part Of: Applicable analysis. Volume 97:Issue 15(2018)
• Page Start: 2686
• Page End: 2719
• Publication Date: 2018-11-18
• Subjects: Nonlinear ill-posed operator equations -- iterative regularization methods -- nonlinear operators on Banach spaces -- source conditions -- stopping index; Primary: 47A52 -- Secondary: 65J15 -- 65J22 -- 65M30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1386785
• Languages: English
• ISSNs: 0003-6811

Abstract

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 .