Analysis of error produced by truncated SVD and Tikhonov regularization methods

The paper considers regularization of inverse solutions to linear problems. We derive the relationship between the error due to regularization and the energy distribution in the observation vector across the width of the singular value spectrum of the linear model used. One result of the analysis is that conditions exist under which no close approximation to the true solution can be found. It follows that a check of these conditions to determine the success of the regularization is important and we feel it should be included in the regularization process. The presentation includes a series of simulations to illustrate the analysis