Regularization of inverse problems by an approximate matrix-function technique

DOI10.1007/s11075-021-01076-yzbMath1490.65067OpenAlexW3153312522MaRDI QIDQ2234483

Fabio Durastante, Marco Donatelli, Stefano Cipolla

Publication date: 19 October 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-021-01076-y

zbMATH Keywords

regularizationinverse problemsKrylov methodsmatrix function

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22)

Uses Software

• Regularization tools
• AIR tools
• mftoolbox
• IR Tools

Cites Work

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• A weighted-GCV method for Lanczos-hybrid regularization
• Arnoldi-Tikhonov regularization methods
• Inverse Toeplitz preconditioners for ill-posed problems
• A unifying approach to abstract matrix algebra preconditioning
• GMRES, L-curves, and discrete ill-posed problems
• Preconditioning linear systems via matrix function evaluation
• A classification scheme for regularizing preconditioners, with application to Toeplitz systems
• Adaptive matrix algebras in unconstrained minimization
• On Krylov projection methods and Tikhonov regularization
• Automatic parameter setting for Arnoldi-Tikhonov methods
• Structure preserving preconditioners for image deblurring
• Regularizing preconditioners by non-stationary iterated Tikhonov with general penalty term
• AIR tools II: algebraic iterative reconstruction methods, improved implementation
• IR tools: a MATLAB package of iterative regularization methods and large-scale test problems
• A rational Arnoldi approach for ill-conditioned linear systems
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Regularizing properties of a class of matrices including the optimal and the superoptimal preconditioners
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• A Bidiagonalization-Regularization Procedure for Large Scale Discretizations of Ill-Posed Problems
• Decay Properties of Spectral Projectors with Applications to Electronic Structure
• Functions of Matrices
• Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring