Iterative Regularization Methods for Nonlinear Ill-Posed Problems

By Barbara Kaltenbacher, Andreas Neubauer, Otmar Scherzer. Radon Series on Computational and Applied Mathematics, 2008

801 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eb8cc98a1e39acf32f5200a71925a2cd8c2b6d38

How researchers see this paper

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

In Civil and Structural Engineering

1. Bernd Hofmann
2. Mark A. Lukas
3. Frank Bauer
4. Ye Zhang
5. Kody J. H. Law
6. M. Iglesias
7. Andrew M. Stuart

In Mathematical Physics

1. Bernd Hofmann
2. Masahiro Yamamoto
3. Kim Knudsen
4. Andrew M. Stuart
5. Barbara Kaltenbacher
6. Matti Lassas
7. Gunther Uhlmann
8. Frank Schöpfer

In Statistics and Probability

1. Kody J. H. Law
2. M. Iglesias
3. Andrew M. Stuart
4. Bernd Hofmann
5. Mark A. Lukas
6. Frank Bauer
7. Ye Zhang
8. Masahiro Yamamoto

Citations in the corpus

• On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems (2010, background): “On the other hand, the case c11⁄4 1, c21⁄4 0 characterized by a tangential cone condition is frequently discussed in the theory of iterative regularization (cf [22, Chapter 11] and [24]).”
• On the second-order asymptotical regularization of linear ill-posed inverse problems (2018, positive): “Therefore, in practice accelerating strategies are usually used; see [3, 7] and references therein for details.”
• Comparing parameter choice methods for regularization of ill-posed problems (2011, methodology): “The discrepancy principle has also been applied to and analyzed for various iterative regularization methods for linear and nonlinear problems in the deterministic setting, including Landweber iteration, the conjugate gradient algorithm and the iteratively regularized Gauss–Newton method (see [41, 6”
• REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “Iterative regularization of both linear and nonlinear inverse problems and convergence rates are discussed in Hilbert space setting in [9, 33, 35, 63, 64] and in Banach space setting in [34, 43 , 44, 47, 74, 75, 76].”
• Ensemble Kalman methods for inverse problems (2012, methodology): “The discrepancy principle, for example, provides a stopping criterion that will ensure the convergence and regularizing properties of iterative techniques such as the Landweber iteration, Levenberg–Marquardt and the iteratively regularized Gauss–Newton [23].”
• Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems (2009, background): “We point out that so far, convergence of the IRGNM has been studied under somewhat stronger conditions on F even in the Hilbert space setting, compare [16, 18].”