The rate of convergence of conjugate gradients
Numerische Mathematik
The regularizing properties of the adjoint gradient method in ill-posed problems
USSR Computational Mathematics and Mathematical Physics
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
Test matrices for regularization methods
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
Stability of Conjugate Gradient and Lanczos Methods for Linear Least Squares Problems
SIAM Journal on Matrix Analysis and Applications
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
The mathematics of computerized tomography
The mathematics of computerized tomography
Large scale least squares scattered data fitting
Applied Numerical Mathematics
Reconstruction of capacitance tomography images of simulated two-phase flow regimes
Applied Numerical Mathematics
Iterative methods for ill-posed problems and semiconvergent sequences
Journal of Computational and Applied Mathematics
An adaptive pruning algorithm for the discrete L-curve criterion
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
A new L-curve for ill-posed problems
Journal of Computational and Applied Mathematics
SAR image regularization with fast approximate discrete minimization
IEEE Transactions on Image Processing
Convex constrained optimization for large-scale generalized Sylvester equations
Computational Optimization and Applications
Old and new parameter choice rules for discrete ill-posed problems
Numerical Algorithms
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The Conjugate Gradient Method (CG) has an intrinsic regularization property when applied to systems of linear equations with ill-conditioned matrices. This regularization property is specially useful when either the right-hand side or the coefficient matrix, or both are given with errors. The regularization parameter is the iteration number, and in order to find this parameter, the L-curve is used. Here we present a novel method to find the corner of the L-curve, that determines the regularizing iteration number. Numerical results on the collection of test problems [SIAM J. Sci. Comput. 16 (1995) 506-512] are given to illustrate the potentiality of the method.