TY - RPRT

T1 - An Adaptive Pruning Algorithm for the Discrete L-Curve Criterion

AU - Hansen, Per Christian

AU - Jensen, Toke Koldborg

AU - Rodriguez, Giuseppe

PY - 2004

Y1 - 2004

N2 - We describe a robust and adaptive implementation of the L-curve criterion, i.e., for locating the corner of a discrete L-curve consisting of a log-log plot of corresponding residual 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 pre-defined 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 algoritms and demonstrate its robustness by numerical examples.

AB - We describe a robust and adaptive implementation of the L-curve criterion, i.e., for locating the corner of a discrete L-curve consisting of a log-log plot of corresponding residual 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 pre-defined 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 algoritms and demonstrate its robustness by numerical examples.

KW - L-curve criterion

KW - parameter-choice method.

KW - regularization

KW - Discrete ill-posed problems

M3 - Report

BT - An Adaptive Pruning Algorithm for the Discrete L-Curve Criterion

ER -