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

A Van Der Sluis,H.A. van der Vorst

doi:10.1016/0024-3795(90)90215-x

A Van Der Sluis, H.A. van der Vorst

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https://doi.org/10.1016/0024-3795(90)90215-x

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Journal: Linear Algebra and Its Applications	Publication Date: Mar 1, 1990
Citations: 91	License type: publisher-specific-oa

Affiliation: Utrecht University

Abstract

SIRT 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.

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