The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
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 triangle method for finding the corner of the L-curve
Applied Numerical Mathematics
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
Old and new parameter choice rules for discrete ill-posed problems
Numerical Algorithms
FGMRES for linear discrete ill-posed problems
Applied Numerical Mathematics
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We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log-log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples.