A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method

A new technique to find the optimization parameter in TSVD regularization method is based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter, then the above-mentioned curve is also discrete. In this paper we present a mathematical analysis of this curve, showing that the curve has L-shaped path very similar to that of the classical L-curve and its corner point can represent the optimization regularization parameter very well. In order to find the corner point of the L-curve (optimization parameter), two methods are applied: pruning and triangle. Numerical results show that in the considered test problems the new curve is better than the classical L-curve.