Computational methods for large-scale inverse problems: a survey on hybrid projection methods

J Chung, S Gazzola - Siam Review, 2024 - SIAM
This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …

GCV for Tikhonov regularization by partial SVD

C Fenu, L Reichel, G Rodriguez, H Sadok - BIT Numerical Mathematics, 2017 - Springer
Tikhonov regularization is commonly used for the solution of linear discrete ill-posed
problems with error-contaminated data. A regularization parameter that determines the …

Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches

S Gazzola, M Sabaté Landman - GAMM‐Mitteilungen, 2020 - Wiley Online Library
Large‐scale linear systems coming from suitable discretizations of linear inverse problems
are challenging to solve. Indeed, since they are inherently ill‐posed, appropriate …

An iterative method for Tikhonov regularization with a general linear regularization operator

ME Hochstenbach, L Reichel - The Journal of Integral Equations and …, 2010 - JSTOR
Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed
problems with error-contaminated data. A regularization operator and a suitable value of a …

[HTML][HTML] Arnoldi–Tikhonov regularization methods

B Lewis, L Reichel - Journal of Computational and Applied Mathematics, 2009 - Elsevier
Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented
by determining a partial Lanczos bidiagonalization of the matrix of the given system of …

Tikhonov regularization based on generalized Krylov subspace methods

L Reichel, F Sgallari, Q Ye - Applied Numerical Mathematics, 2012 - Elsevier
We consider Tikhonov regularization of large linear discrete ill-posed problems with a
regularization operator of general form and present an iterative scheme based on a …

[PDF][PDF] Simple square smoothing regularization operators

L Reichel, Q Ye - Electron. Trans. Numer. Anal, 2009 - core.ac.uk
Tikhonov regularization of linear discrete ill-posed problems often is applied with a finite
difference regularization operator that approximates a low-order derivative. These operators …

Square regularization matrices for large linear discrete ill‐posed problems

M Donatelli, A Neuman… - Numerical Linear Algebra …, 2012 - Wiley Online Library
Large linear discrete ill‐posed problems with contaminated data are often solved with the
aid of Tikhonov regularization. Commonly used regularization matrices are finite difference …

[HTML][HTML] Simplified GSVD computations for the solution of linear discrete ill-posed problems

L Dykes, L Reichel - Journal of Computational and Applied Mathematics, 2014 - Elsevier
The generalized singular value decomposition (GSVD) often is used to solve Tikhonov
regularization problems with a regularization matrix without exploitable structure. This paper …

Regularization matrices determined by matrix nearness problems

G Huang, S Noschese, L Reichel - Linear Algebra and Its Applications, 2016 - Elsevier
This paper is concerned with the solution of large-scale linear discrete ill-posed problems
with error-contaminated data. Tikhonov regularization is a popular approach to determine …