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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 3: Inverse Problems and Regularization Theory. Guest Editor: Jin Cheng, Masahiro Yamamoto, Shuai Lu, Jens Flemming and Stephan W. Anzengruber
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Articles

About a deficit in low-order convergence rates on the example of autoconvolution

Steven BürgerFaculty of Mathematics, TU Chemnitz, Reichenhainer Str. 41, Chemnitz09107, Germany.Correspondence[email protected]
&
Bernd HofmannFaculty of Mathematics, TU Chemnitz, Reichenhainer Str. 41, Chemnitz09107, Germany.
Pages 477-493 | Received 17 Dec 2013, Accepted 16 Jan 2014, Published online: 17 Feb 2014

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Steven Bürger & Peter Mathé. (2017) Discretized Lavrent’ev regularization for the autoconvolution equation. Applicable Analysis 96:10, pages 1618-1637.
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Articles from other publishers (15)

Bernd Hofmann, Frank Werner & Yu Deng. (2023) On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case. Inverse Problems 39:6, pages 065012.
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Bin Fan & Chuanju Xu. (2021) Inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems * . Inverse Problems 37:4, pages 045007.
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Frank Werner & Bernd Hofmann. (2019) Convergence analysis of (statistical) inverse problems under conditional stability estimates. Inverse Problems 36:1, pages 015004.
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Daniel Gerth, Bernd Hofmann & Christopher Hofmann. 2020. Inverse Problems and Related Topics. Inverse Problems and Related Topics 177 203 .
Michael V. Klibanov, Dinh-Liem Nguyen & Loc H. Nguyen. (2019) A Coefficient Inverse Problem with a Single Measurement of Phaseless Scattering Data. SIAM Journal on Applied Mathematics 79:1, pages 1-27.
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Robert Beinert & Kristian Bredies. (2019) Non-convex regularization of bilinear and quadratic inverse problems by tensorial lifting. Inverse Problems 35:1, pages 015002.
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Simon Hubmer & Ronny Ramlau. (2018) Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional. Inverse Problems 34:9, pages 095003.
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Bernd Hofmann & Robert Plato. (2018) On ill-posedness concepts, stable solvability and saturation. Journal of Inverse and Ill-posed Problems 26:2, pages 287-297.
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Qinian Jin & Wei Wang. (2018) Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule. Inverse Problems 34:3, pages 035001.
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Michael V. Klibanov, Nikolay A. Koshev, Dinh-Liem Nguyen, Loc H. Nguyen, Aaron Brettin & Vasily N. Astratov. (2018) A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data. SIAM Journal on Imaging Sciences 11:4, pages 2339-2367.
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Jens FlemmingJens Flemming. 2018. Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization. Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization 97 105 .
Jens FlemmingJens Flemming. 2018. Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization. Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization 31 53 .
Steven Bürger, Jens Flemming & Bernd Hofmann. (2016) On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation. Inverse Problems 32:10, pages 104006.
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Stephan W Anzengruber, Steven Bürger, Bernd Hofmann & Günter Steinmeyer. (2016) Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization. Inverse Problems 32:3, pages 035002.
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Simon Birkholz, Günter Steinmeyer, Sebastian Koke, Daniel Gerth, Steven Bürger & Bernd Hofmann. (2015) Phase retrieval via regularization in self-diffraction-based spectral interferometry. Journal of the Optical Society of America B 32:5, pages 983.
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