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Enhanced choice of the parameters in an iteratively regularized NewtonLandweber iteration in Banach space
1.  AlpenAdriaUniversität Klagenfurt, Universitätsstraße 6567, 9020 Klagenfurt 
2.  Università di Bologna, Piazza Porta S. Donato, 5, 40127  Bologna, Italy 
References:
[1] 
A. B. Bakushinsky and M. Yu. Kokurin, Iterative methods for approximate solution of inverse problems,, Springer, (2004). 
[2] 
M. Burger and S. Osher, Convergence rates of convex variational regularization,, Inverse Problems, 20 (2004), 1411. 
[3] 
C. Clason and B. Jin, A semismooth Newton method for nonlinear parameter identification problems with impulsive noise,, SIAM J. Imaging Sci, 5 (2012), 505. 
[4] 
M. Hanke, A. Neubauer, and O. Scherzer, A convergence analysis of the Landweber iteration for nonlinear illposed problems,, Numer. Math., 72 (1995), 21. 
[5] 
T. Hein and B. Hofmann, Approximate source conditions for nonlinear illposed problems  chances and limitations,, Inverse Problems, (2009). 
[6] 
T. Hein and K. S. Kazimierski, Accelerated Landweber iteration in Banach spaces,, Inverse Problems, (2010). 
[7] 
T. Hein and K. S. Kazimierski, Modified Landweber iteration in Banach spaces  convergence and convergence rates,, Numerical Functional Analysis and Optimization, 31 (2010), 1158. 
[8] 
B. Hofmann, B. Kaltenbacher, C. Pöschl, and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with nonsmooth operators,, Inverse Problems, 23 (2007), 987. 
[9] 
B. Kaltenbacher and I. Tomba, Convergence rates for an iteratively regularized NewtonLandweber iteration in Banach space,, Inverse Problems, (2013). 
[10] 
B. Kaltenbacher and I. Tomba, Enhanced choice of the parameters in an iteratively regularized Newton Landweber iteration in Banach space,, arXiv:1408.5026 [math.NA], (2014). 
[11] 
Q. Jin, Inexact NewtonLandweber iteration for solving nonlinear inverse problems in Banach spaces,, Inverse Problems, (2012). 
[12] 
Q. Jin and L.Stals, Nonstationary iterated Tikhonov regularization for illposed problems in Banach spaces,, Inverse Problems, (2012). 
[13] 
B. Kaltenbacher, Convergence rates for the iteratively regularized Landweber iteration in Banach space,, Proceedings of the 25th IFIP TC7 Conference on System Modeling and Optimization, (2013), 38. 
[14] 
B. Kaltenbacher and B. Hofmann, Convergence rates for the iteratively regularized gaussnewton method in Banach spaces,, Inverse Problems, (2010). 
[15] 
B. Kaltenbacher, A. Neubauer, and O. Scherzer, Iterative Regularization Methods for Nonlinear Illposed Problems,, de Gruyter, (2007). 
[16] 
B. Kaltenbacher, F. Schöpfer, and T. Schuster, Convergence of some iterative methods for the regularization of nonlinear illposed problems in Banach spaces,, Inverse Problems, (2009). 
[17] 
A. Neubauer, T. Hein, B. Hofmann, S. Kindermann, and U. Tautenhahn, Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces,, Appl. Anal., 89 (2010), 1729. 
[18] 
A. Rieder, On convergence rates of inexact Newton regularizations,, Numer. Math. 88 (2001), 88 (2001), 347. 
[19] 
A. Rieder, Inexact Newton regularization using conjugate gradients as inner iteration,, SIAM J. Numer. Anal. 43 (2005), 43 (2005), 604. 
[20] 
O. Scherzer, A modified Landweber iteration for solving parameter estimation problems,, Appl. Math. Optim., 38 (1998), 45. 
[21] 
F. Schöpfer, A. K. Louis, and T. Schuster, Nonlinear iterative methods for linear illposed problems in Banach spaces,, Inverse Problems, 22 (2006), 311. 
[22] 
T. Schuster, B. Kaltenbacher, B. Hofmann, and K. Kazimierski, Regularization Methods in Banach Spaces,, de Gruyter, (2012). 
[23] 
Z.B. Xu and G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces,, Journal of Mathematical Analysis and Applications, 157 (1991), 189. 
show all references
References:
[1] 
A. B. Bakushinsky and M. Yu. Kokurin, Iterative methods for approximate solution of inverse problems,, Springer, (2004). 
[2] 
M. Burger and S. Osher, Convergence rates of convex variational regularization,, Inverse Problems, 20 (2004), 1411. 
[3] 
C. Clason and B. Jin, A semismooth Newton method for nonlinear parameter identification problems with impulsive noise,, SIAM J. Imaging Sci, 5 (2012), 505. 
[4] 
M. Hanke, A. Neubauer, and O. Scherzer, A convergence analysis of the Landweber iteration for nonlinear illposed problems,, Numer. Math., 72 (1995), 21. 
[5] 
T. Hein and B. Hofmann, Approximate source conditions for nonlinear illposed problems  chances and limitations,, Inverse Problems, (2009). 
[6] 
T. Hein and K. S. Kazimierski, Accelerated Landweber iteration in Banach spaces,, Inverse Problems, (2010). 
[7] 
T. Hein and K. S. Kazimierski, Modified Landweber iteration in Banach spaces  convergence and convergence rates,, Numerical Functional Analysis and Optimization, 31 (2010), 1158. 
[8] 
B. Hofmann, B. Kaltenbacher, C. Pöschl, and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with nonsmooth operators,, Inverse Problems, 23 (2007), 987. 
[9] 
B. Kaltenbacher and I. Tomba, Convergence rates for an iteratively regularized NewtonLandweber iteration in Banach space,, Inverse Problems, (2013). 
[10] 
B. Kaltenbacher and I. Tomba, Enhanced choice of the parameters in an iteratively regularized Newton Landweber iteration in Banach space,, arXiv:1408.5026 [math.NA], (2014). 
[11] 
Q. Jin, Inexact NewtonLandweber iteration for solving nonlinear inverse problems in Banach spaces,, Inverse Problems, (2012). 
[12] 
Q. Jin and L.Stals, Nonstationary iterated Tikhonov regularization for illposed problems in Banach spaces,, Inverse Problems, (2012). 
[13] 
B. Kaltenbacher, Convergence rates for the iteratively regularized Landweber iteration in Banach space,, Proceedings of the 25th IFIP TC7 Conference on System Modeling and Optimization, (2013), 38. 
[14] 
B. Kaltenbacher and B. Hofmann, Convergence rates for the iteratively regularized gaussnewton method in Banach spaces,, Inverse Problems, (2010). 
[15] 
B. Kaltenbacher, A. Neubauer, and O. Scherzer, Iterative Regularization Methods for Nonlinear Illposed Problems,, de Gruyter, (2007). 
[16] 
B. Kaltenbacher, F. Schöpfer, and T. Schuster, Convergence of some iterative methods for the regularization of nonlinear illposed problems in Banach spaces,, Inverse Problems, (2009). 
[17] 
A. Neubauer, T. Hein, B. Hofmann, S. Kindermann, and U. Tautenhahn, Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces,, Appl. Anal., 89 (2010), 1729. 
[18] 
A. Rieder, On convergence rates of inexact Newton regularizations,, Numer. Math. 88 (2001), 88 (2001), 347. 
[19] 
A. Rieder, Inexact Newton regularization using conjugate gradients as inner iteration,, SIAM J. Numer. Anal. 43 (2005), 43 (2005), 604. 
[20] 
O. Scherzer, A modified Landweber iteration for solving parameter estimation problems,, Appl. Math. Optim., 38 (1998), 45. 
[21] 
F. Schöpfer, A. K. Louis, and T. Schuster, Nonlinear iterative methods for linear illposed problems in Banach spaces,, Inverse Problems, 22 (2006), 311. 
[22] 
T. Schuster, B. Kaltenbacher, B. Hofmann, and K. Kazimierski, Regularization Methods in Banach Spaces,, de Gruyter, (2012). 
[23] 
Z.B. Xu and G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces,, Journal of Mathematical Analysis and Applications, 157 (1991), 189. 
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