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April  2009, 5(2): 175-191. doi: 10.3934/jimo.2009.5.175

Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems

H. D. Scolnik 1, , N. E. Echebest 2, and  M. T. Guardarucci 3,

1. 

Dto. de Computación, Fac. de Ciencias Exactas y Naturales. UBA, Pabellón 1, Ciudad Universitaria, Buenos Aires, C1428EGA, Argentina
2. 

Departamento de Matemática, Fac. de Ciencias Exactas. UNLP, P.O. Box 172. La Plata,1900, Argentina
3. 

Departamento de C. Básicas, Fac. de Ingeniería. UNLP, La Plata, 1900, Argentina

Received  April 2007 Revised  February 2009 Published  April 2009

The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system $ Ax-r=b$. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.
Keywords: minimal norm solution, incomplete oblique projections., Rank-deficient least-squares problems.
Mathematics Subject Classification: Primary: 90C25; Secondary: 90C3.
Citation: H. D. Scolnik, N. E. Echebest, M. T. Guardarucci. Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems. Journal of Industrial and Management Optimization, 2009, 5 (2) : 175-191. doi: 10.3934/jimo.2009.5.175
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