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Numerical Functional Analysis and Optimization Volume 13, 1992 - Issue 5-6
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Original Articles

Regularization with Differential Operators: An Iterative Approach

Martin Hanke Institut für Praktische Mathematik, Universität Karlsruhe, Karlsruhe, D-7500, Germany
Pages 523-540 | Received 01 Jul 1991, Accepted 01 Mar 1992, Published online: 15 May 2007

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Min Zhai, Guolin Liu, Qiuxiang Tao, Zhaoying Jiang & Mingzhen Xin. (2020) A novel approach for regularization matrix construction and its application in SBAS deformation model inversion. International Journal of Remote Sensing 41:10, pages 3708-3722.
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Li Gongsheng & Zuhair Nashed. (2005) A Modified Tikhonov Regularization for Linear Operator Equations. Numerical Functional Analysis and Optimization 26:4-5, pages 543-563.
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Articles from other publishers (19)

Tyler D. Stoffel, Christopher D. Karlgaard, Todd R. White & Thomas K. WestIVIV. (2024) Fusion of In-Flight Aerothermodynamic Heating Sensor Measurements Using Kalman Filtering. Journal of Spacecraft and Rockets 61:2, pages 599-610.
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Abdulaziz Alqahtani, Thomas Mach & Lothar Reichel. (2023) Tikhonov regularization in general form with Chebfun. PAMM 22:1.
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Hongqi Yang & Rong Zhang. (2022) A fast multilevel iteration method for solving linear ill-posed integral equations. Journal of Inverse and Ill-posed Problems 30:3, pages 409-423.
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Silvia Gazzola & Malena Sabaté Landman. (2020) Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches. GAMM-Mitteilungen 43:4.
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Zhen Chen, Tommy H.T. Chan & Andy Nguyen. (2018) Moving force identification based on modified preconditioned conjugate gradient method. Journal of Sound and Vibration 423, pages 100-117.
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S R Arridge, M M Betcke & L Harhanen. (2014) Iterated preconditioned LSQR method for inverse problems on unstructured grids. Inverse Problems 30:7, pages 075009.
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Per Christian Hansen. (2011) Oblique projections and standard‐form transformations for discrete inverse problems. Numerical Linear Algebra with Applications 20:2, pages 250-258.
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Radu Ioan Boţ & Torsten Hein. (2012) Iterative regularization with a general penalty term—theory and application to L 1 and TV regularization . Inverse Problems 28:10, pages 104010.
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Markus Hegland & Bernd Hofmann. (2011) Errors of regularisation under range inclusions using variable Hilbert scales. Inverse Problems & Imaging 5:3, pages 619-643.
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Andreas KirschAndreas Kirsch. 2011. An Introduction to the Mathematical Theory of Inverse Problems. An Introduction to the Mathematical Theory of Inverse Problems 23 61 .
L. K. Babadzhanyants, A. V. Voitylov, V. V. Voitylov & A. A. Trusov. (2010) Analysis of polydispersity of macromolecular and nanodisperse systems by electrooptical methods. Polymer Science Series C 52:1, pages 93-104.
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Per Christian Hansen, Henning Osholm Sørensen, Zsuzsanna Sükösd & Henning Friis Poulsen. (2009) Reconstruction of Single-Grain Orientation Distribution Functions for Crystalline Materials. SIAM Journal on Imaging Sciences 2:2, pages 593-613.
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Daniela Calvetti & Erkki Somersalo. (2005) Priorconditioners for linear systems. Inverse Problems 21:4, pages 1397-1418.
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D. Calvetti, L. Reichel & A. Shuibi. (2005) Invertible smoothing preconditioners for linear discrete ill-posed problems. Applied Numerical Mathematics 54:2, pages 135-149.
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J. F. Power. (2002) Inverse problem theory in the optical depth profilometry of thin films. Review of Scientific Instruments 73:12, pages 4057-4141.
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M. Thamban Nair. (2002) Optimal order results for a class of regularization methods using unbounded operators. Integral Equations and Operator Theory 44:1, pages 79-92.
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Misha E. Kilmer & Dianne P. O'Leary. (1999) Pivoted Cauchy-Like Preconditioners for Regularized Solution of Ill-Posed Problems. SIAM Journal on Scientific Computing 21:1, pages 88-110.
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Per Christian Hansen. (1994) REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms 6:1, pages 1-35.
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P C Hansen. (1992) Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Inverse Problems 8:6, pages 849-872.
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