A Regularization Parameter in Discrete Ill-Posed Problems

The Tikhonov regularization method for discrete ill-posed problems is considered. For the practical choice of the regularization parameter α, some authors use a plot of the norm of the regularized solution versus the norm of the residual vector for all α considered. This paper contains an analysis of the shape of this plot and gives atheoretical justification for choosing the regularization parameter so it is related to the “{ L ” of the plot considered in the logarithmic scale. Moreover, a new criterion for choosing a is introduced (independent of the shape of the plot) which gives a new interpretation of the “corner criterion” mentioned above. The existence of “L-corner” is discussed.