Nonlinear iterative methods for linear ill-posed problems in Banach spaces

By Frank Schöpfer, Alfred K. Louis, Tal Schuster. 2006

166 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/12502514f75d02853ed35ae26c041ca0984ea45a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Bangti Jin
2. Bernd Hofmann
3. Peter Maass
4. Martin Burger
5. Barbara Kaltenbacher
6. Martin Benning
7. Frank Schöpfer
8. Tal Schuster

In Mathematical Physics

1. Bangti Jin
2. Peter Maass
3. Bernd Hofmann
4. Martin Burger
5. Martin Benning
6. Masahiro Yamamoto
7. Barbara Kaltenbacher
8. Frank Schöpfer

In Numerical Analysis

1. Bangti Jin
2. Martin Burger
3. Peter Maass
4. Martin Benning
5. Tal Schuster
6. Frank Schöpfer
7. Bernd Hofmann
8. Barbara Kaltenbacher

Citations in the corpus

• Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems (2009, methodology): “3 in [23] to the nonlinear case, the convergence result theorem 2.”
• An iterative regularization method for the solution of the split feasibility problem in Banach spaces (2008, methodology): “Hierbei verbessern und ergänzen wir unter Verwendung des oben erwähnten Zerlegungssatzes unsere Arbeit in [46], wo wir schon die starke Konvergenz dieses Verfahrens zeigen konnten.”
• Regularization with non-convex separable constraints (2009, unknown): “Also iterative methods have been analyzed [35].”
• An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems (2010, background): “MSC2000 subject classification: 47J06, 65J20, 47A52, 49N45 Keywords: Ill-posed problems, Tikhonov regularization, convergence rates, variational inequalities, source conditions, distance function, structure of nonlinearity, generalized Young inequality.”
• Modern regularization methods for inverse problems (2018, methodology): “We refer to [336, 345, 21, 237, 345, 219] for further discussion In the following sections we discuss extensions of the iterative regularization methods presented in Section 6 to nonlinear inverse problems.”
• An analysis of electrical impedance tomography with applications to Tikhonov regularization (2012, methodology): “, iterative regularization methods such as Landweber and Gauss-Newton methods in Banach spaces [50, 5, 35], might also be justified using the presented analytical results.”
• On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems (2010, result): “For recent results we refer to the monograph [29] and in an exemplary manner to the papers [3, 4, 10, 12, 13, 14, 19, 21, 22, 26, 27, 28, 30, 31, 33] as well as to the thesis [24].”