References
- Bakushinsky AB, Kokurin MY. Iterative methods for approximate solutions of inverse problems. Dordrecht: Springer; 2004. (Mathematics and Its Applications (New York); vol. 57).
- Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer; 1996.
- Kaltenbacher B, Neubauer A, Scherzer O. Iterative regularization methods for nonlinear ill-posed problems. Berlin: de Gruyter; 2008.
- Hanke M, Neubauer A, Scherzer O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer Math. 1995;72:21–37.
- Mahale P, Nair MT. A simplified generalized Gauss-Newton method for nonlinear ill-posed problems. Math Comput. 2009;78(265):171–184.
- Mahale P, Nair MT. Iterated Lavrentiev regularization for nonlinear ill-posed problems. ANZIAM J. 2009;51(2):191–217.
- Mahale P, Nair MT. Tikhonov regularization of nonlinear ill-posed equations under general source condition. J Inverse Ill-Posed Problems. 2007;15(8):215–829.
- Jin Q. A general convergence analysis of some Newton-type methods for nonlinear inverse problems. SIAM J Numer Anal. 2011;49:549–573.
- Jin Q, Tautenhahn U. On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems. Numer Math. 2009;111:509–558.
- Rieder A. On convergence rates of inexact Newton regularizations. Numer Math. 2001;88:347–365.
- Hanke M. A regularizing Levenberg–Marquardt scheme with applications to inverse groundwater filtration problems. Inverse Probl. 1997;13:79–95.
- Jin Q. On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems. Numer Math. 2010;115:229–259.
- Clason C, Jin B. Semi-smooth Newton method for nonlinear parameter identification problems with impulsive noise. SIAM J Imaging Sci. 2012;5:505–536.
- Kaltenbacher B, Tomba I. Convergence rates for an iteratively regularized Newton-Landweber iteration in Banach space. Inverse Probl. 2013;29:025010.
- Jin Q. Inexact Newton-Landweber iteration for solving nonlinear inverse problems in Banach spaces. Inverse Probl. 2012;28:065002.
- Tibshirani R. Regression shrinkage and selection via the Lasso. J R Stat Soc Ser B. 1996;58:267–288.
- Rudin L, Osher S, Fatemi C. Nonlinear total variation based noise removal algorithm. Phys D. 1992;60:259–268.
- Jin Q. On the regularizing Levenberg-Marquardt scheme in Banach spaces. preprint (2011). https://maths-people.anu.edu.au/jinq/Jin2011c.pdf.
- Scherzer O. Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems. J Math Anal Appl. 1995;194(3):911–933.
- Jin Q, Yang H. Levenberg-Marquardt method in Banach spaces with general convex regularization terms. Numer Math. 2016;133:655–684.
- Cioranescu I. Geometry of Banach spaces, duality mappings and nonlinear problems. Dordrecht: Kluwer; 1990.
- Xu ZB, Roach GF. Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces. J Math Anal Appl. 1991;157:189–210.
- Schöpfer F, Louis AK, Schuster T. Nonlinear iterative methods for linear ill-posed problems in Banach spaces. Inverse Probl. 2006;22:311–329.
- Clason C, Nhu VH. Bouligand–Landweber iteration for a non-smooth ill-posed problem. Numer Math. 2019;142:789–832.
- Jin Q, Wang W. Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals. Inverse Probl. 2013;29:085011.
- Kaltenbacher B, Schöpfer F, Schuster T. Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems. Inverse Probl. 2009;25(6):065003.