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Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space
1. | Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65-67, 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). Google Scholar |
[2] |
M. Burger and S. Osher, Convergence rates of convex variational regularization,, Inverse Problems, 20 (2004), 1411. Google Scholar |
[3] |
C. Clason and B. Jin, A semi-smooth Newton method for nonlinear parameter identification problems with impulsive noise,, SIAM J. Imaging Sci, 5 (2012), 505. Google Scholar |
[4] |
M. Hanke, A. Neubauer, and O. Scherzer, A convergence analysis of the Landweber iteration for nonlinear ill-posed problems,, Numer. Math., 72 (1995), 21. Google Scholar |
[5] |
T. Hein and B. Hofmann, Approximate source conditions for nonlinear ill-posed problems - chances and limitations,, Inverse Problems, (2009). Google Scholar |
[6] |
T. Hein and K. S. Kazimierski, Accelerated Landweber iteration in Banach spaces,, Inverse Problems, (2010). Google Scholar |
[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. Google Scholar |
[8] |
B. Hofmann, B. Kaltenbacher, C. Pöschl, and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators,, Inverse Problems, 23 (2007), 987. Google Scholar |
[9] |
B. Kaltenbacher and I. Tomba, Convergence rates for an iteratively regularized Newton-Landweber iteration in Banach space,, Inverse Problems, (2013). Google Scholar |
[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). Google Scholar |
[11] |
Q. Jin, Inexact Newton-Landweber iteration for solving nonlinear inverse problems in Banach spaces,, Inverse Problems, (2012). Google Scholar |
[12] |
Q. Jin and L.Stals, Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces,, Inverse Problems, (2012). Google Scholar |
[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. Google Scholar |
[14] |
B. Kaltenbacher and B. Hofmann, Convergence rates for the iteratively regularized gauss-newton method in Banach spaces,, Inverse Problems, (2010). Google Scholar |
[15] |
B. Kaltenbacher, A. Neubauer, and O. Scherzer, Iterative Regularization Methods for Nonlinear Ill-posed Problems,, de Gruyter, (2007). Google Scholar |
[16] |
B. Kaltenbacher, F. Schöpfer, and T. Schuster, Convergence of some iterative methods for the regularization of nonlinear ill-posed problems in Banach spaces,, Inverse Problems, (2009). Google Scholar |
[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. Google Scholar |
[18] |
A. Rieder, On convergence rates of inexact Newton regularizations,, Numer. Math. 88 (2001), 88 (2001), 347. Google Scholar |
[19] |
A. Rieder, Inexact Newton regularization using conjugate gradients as inner iteration,, SIAM J. Numer. Anal. 43 (2005), 43 (2005), 604. Google Scholar |
[20] |
O. Scherzer, A modified Landweber iteration for solving parameter estimation problems,, Appl. Math. Optim., 38 (1998), 45. Google Scholar |
[21] |
F. Schöpfer, A. K. Louis, and T. Schuster, Nonlinear iterative methods for linear ill-posed problems in Banach spaces,, Inverse Problems, 22 (2006), 311. Google Scholar |
[22] |
T. Schuster, B. Kaltenbacher, B. Hofmann, and K. Kazimierski, Regularization Methods in Banach Spaces,, de Gruyter, (2012). Google Scholar |
[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. Google Scholar |
show all references
References:
[1] |
A. B. Bakushinsky and M. Yu. Kokurin, Iterative methods for approximate solution of inverse problems,, Springer, (2004). Google Scholar |
[2] |
M. Burger and S. Osher, Convergence rates of convex variational regularization,, Inverse Problems, 20 (2004), 1411. Google Scholar |
[3] |
C. Clason and B. Jin, A semi-smooth Newton method for nonlinear parameter identification problems with impulsive noise,, SIAM J. Imaging Sci, 5 (2012), 505. Google Scholar |
[4] |
M. Hanke, A. Neubauer, and O. Scherzer, A convergence analysis of the Landweber iteration for nonlinear ill-posed problems,, Numer. Math., 72 (1995), 21. Google Scholar |
[5] |
T. Hein and B. Hofmann, Approximate source conditions for nonlinear ill-posed problems - chances and limitations,, Inverse Problems, (2009). Google Scholar |
[6] |
T. Hein and K. S. Kazimierski, Accelerated Landweber iteration in Banach spaces,, Inverse Problems, (2010). Google Scholar |
[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. Google Scholar |
[8] |
B. Hofmann, B. Kaltenbacher, C. Pöschl, and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators,, Inverse Problems, 23 (2007), 987. Google Scholar |
[9] |
B. Kaltenbacher and I. Tomba, Convergence rates for an iteratively regularized Newton-Landweber iteration in Banach space,, Inverse Problems, (2013). Google Scholar |
[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). Google Scholar |
[11] |
Q. Jin, Inexact Newton-Landweber iteration for solving nonlinear inverse problems in Banach spaces,, Inverse Problems, (2012). Google Scholar |
[12] |
Q. Jin and L.Stals, Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces,, Inverse Problems, (2012). Google Scholar |
[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. Google Scholar |
[14] |
B. Kaltenbacher and B. Hofmann, Convergence rates for the iteratively regularized gauss-newton method in Banach spaces,, Inverse Problems, (2010). Google Scholar |
[15] |
B. Kaltenbacher, A. Neubauer, and O. Scherzer, Iterative Regularization Methods for Nonlinear Ill-posed Problems,, de Gruyter, (2007). Google Scholar |
[16] |
B. Kaltenbacher, F. Schöpfer, and T. Schuster, Convergence of some iterative methods for the regularization of nonlinear ill-posed problems in Banach spaces,, Inverse Problems, (2009). Google Scholar |
[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. Google Scholar |
[18] |
A. Rieder, On convergence rates of inexact Newton regularizations,, Numer. Math. 88 (2001), 88 (2001), 347. Google Scholar |
[19] |
A. Rieder, Inexact Newton regularization using conjugate gradients as inner iteration,, SIAM J. Numer. Anal. 43 (2005), 43 (2005), 604. Google Scholar |
[20] |
O. Scherzer, A modified Landweber iteration for solving parameter estimation problems,, Appl. Math. Optim., 38 (1998), 45. Google Scholar |
[21] |
F. Schöpfer, A. K. Louis, and T. Schuster, Nonlinear iterative methods for linear ill-posed problems in Banach spaces,, Inverse Problems, 22 (2006), 311. Google Scholar |
[22] |
T. Schuster, B. Kaltenbacher, B. Hofmann, and K. Kazimierski, Regularization Methods in Banach Spaces,, de Gruyter, (2012). Google Scholar |
[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. Google Scholar |
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