SIRT- and CG-type methods for the iterative solution of sparse linear least-squares problems

AbstractSIRT and CG-type methods have been successfully employed for the approximate solution of least-squares problems arising in tomography. In this paper we study and compare their convergence and regularization properties. It is pointed out that SIRT methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system, whereas CG-type methods do not. For a large class of model problems it is shown that virtually the same solutions as obtained by SIRT methods can be obtained by applying a CG-type method to a properly rescaled system, but with an amount of work proportional to the square root of the amount of work with SIRT