Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization

Matrix computations

1983 • 31,414 citations

Spline Models for Observational Data.

1991 • 5,272 citations

Regularization of Inverse Problems

1996 • 5,174 citations

Analysis of Discrete Ill-Posed Problems by Means of the L-Curve

1992 • 3,619 citations

Spline Models for Observational Data

1990 • 3,507 citations

Smoothing noisy data with spline functions

1978 • 3,289 citations

Numerical methods for least squares problems

1996 • 3,158 citations

Numerical Methods for Least Squares Problems

1996 • 2,964 citations

Rank-Deficient and Discrete Ill-Posed Problems

1998 • 2,734 citations

Solution of incorrectly formulated problems and the regularization method

1963 • 2,355 citations

Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion

1987 • 2,196 citations

A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

1962 • 2,001 citations

Digital image restoration

1997 • 1,681 citations

Iterative Methods for Total Variation Denoising

1996 • 1,051 citations

Generalizing the Singular Value Decomposition

1976 • 627 citations

A Comparison of GCV and GML for Choosing the Smoothing Parameter in the Generalized Spline Smoothing Problem

1985 • 513 citations

Inference and Asymptotics

2017 • 512 citations

Least Squares Methods for Ill-Posed Problems with a Prescribed Bound

1970 • 502 citations

Presentations of faithful d.g. near-rings

1980 • 498 citations

On a New Method of Graduation

1922 • 461 citations

Conjugate Gradient Type Methods for Ill-Posed Problems

2017 • 417 citations

Algorithms for the regularization of ill-conditioned least squares problems

1977 • 304 citations

Error bounds for tikhonov regularization in hilbert scales

1984 • 243 citations

Generalized inverses of linear operators

1977 • 185 citations

Minimizing GCV/GML Scores with Multiple Smoothing Parameters via the Newton Method

1991 • 182 citations

The Stability of Inverse Problems

1980 • 156 citations

A Primer on Integral Equations of the First Kind

1991 • 155 citations

Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion

1984 • 149 citations

Computing the Generalized Singular Value Decomposition

1986 • 135 citations

Asymptotic Inference for Mixture Models by Using Data-Dependent Priors

2000 • 124 citations

A General Heuristic for Choosing the Regularization Parameter in Ill-Posed Problems

1996 • 115 citations

The regularizing properties of the adjoint gradient method in ill-posed problems

1986 • 102 citations

Computing the CS and the generalized singular value decompositions

1985 • 96 citations

On $M$-Processes and $M$-Estimation

1989 • 93 citations

Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix

1955 • 91 citations

ON ILL-POSED PROBLEMS AND THE METHOD OF CONJUGATE GRADIENTS

1987 • 84 citations

Projection filter, Wiener filter, and Karhunen-Loève subspaces in digital image restoration

1986 • 73 citations

Solving Systems of Linear Equations With a Positive Definite, Symmetric, but Possibly Ill-Conditioned Matrix

1955 • 63 citations

PET regularization by envelope guided conjugate gradients

1996 • 46 citations

Superfast algorithms for Cauchy-like matrix computations and extensions

2000 • 32 citations

A method for computing the generalized singular value decomposition

1983 • 30 citations

On the continuity of generalized inverses of linear operators in Hilbert spaces

1997 • 26 citations

Regularization of Ill-Posed Problems by Envelope Guided Conjugate Gradients

1997 • 23 citations

Invited review article (C. Musès) ‐ Wiener’s paper not in the collected works: The history and prehistory of cybernetics

1998 • 2 citations

Deleted Work

1955 • 0 citations