On the incomplete oblique projections method for solving box constrained least squares problems
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The aim of this paper is to extend the applicability of the incomplete oblique projections method (IOP) previously introduced by the authors for solving inconsistent linear systems to the box constrained case. The new algorithm employs incomplete projections onto the set of solutions of the augmented system Ax − r = b, together with the box constraints, based on a scheme similar to the one of IOP, adding the conditions for accepting an approximate solution in the box. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known methods.
KeywordsInconsistent systems Box constrained Incomplete projections
Mathematics Subject Classification (2010)65F10
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- 2.Browne, J.A., Herman, G.T., Odhner, D.: SNARK93: A Programming System for Image Reconstruction from Projections. Department of Radiology, University of Pennsylvania, Medical Image Processing Group. Technical Report MIPG198 (1993)Google Scholar
- 9.Combettes, P.L.: Construction d’un point fixe commun a famille de contractions fermes. C.R. Acad. Sci. Paris, Ser. I Math. 320 (1995)Google Scholar
- 10.Csiszár, I., Tusnády, G.: Information geometry and alternating minimization procedures. Stat. Decis. Suppl. 1, 205–237 (1984)Google Scholar