EFFICIENT ESTIMATION OF THE REGULARIZATION PARAMETERS VIA L-CURVE METHOD FOR TOTAL LEAST SQUARES PROBLEMS

EFFICIENT ESTIMATION OF THE REGULARIZATION PARAMETERS VIA L-CURVE METHOD FOR TOTAL LEAST SQUARES PROBLEMS

The L-curve method is a parametric plot of interrelation between the residual norm of the least squares problem and the solution norm. However, the L-curve method may be hard to apply to the total least squares problem due to its no closed form solution of the regularized total least squares problems. Thus the sequence of the solution norm under the fixed regularization parameter and its corresponding residual need to be found with an efficient manner. In this paper, we suggest an efficient algorithm to find the sequence of the solutions and its residual in order to plot the L-curve for the total least squares problems. In the numerical experiments, we present that the proposed algorithm successfully and efficiently plots fairly 'L' like shape for some practical regularized total least squares problems.