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An Accelerated Iterative Method with Diagonally Scaled Oblique Projections for Solving Linear Feasibility Problems

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Listed:
  • N. Echebest
  • M. Guardarucci
  • H. Scolnik
  • M. Vacchino

Abstract

The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate x k+1 by projecting the current point x k onto a separating hyperplane generated by a given linear combination of the original hyperplanes or halfspaces. In Scolnik et al. (2001, 2002a) and Echebest et al. (2004) acceleration schemes for solving systems of linear equations and inequalities respectively were introduced, within a PAM like framework. In this paper we apply those schemes in an algorithm based on oblique projections reflecting the sparsity of the matrix of the linear system to be solved. We present the corresponding theoretical convergence results which are a generalization of those given in Echebest et al. (2004). We also present the numerical results obtained applying the new scheme to two algorithms introduced by Garcí a-Palomares and González-Castaño (1998) and also the comparison of its efficiency with that of Censor and Elfving (2002). Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • N. Echebest & M. Guardarucci & H. Scolnik & M. Vacchino, 2005. "An Accelerated Iterative Method with Diagonally Scaled Oblique Projections for Solving Linear Feasibility Problems," Annals of Operations Research, Springer, vol. 138(1), pages 235-257, September.
    • Handle: RePEc:spr:annopr:v:138:y:2005:i:1:p:235-257:10.1007/s10479-005-2456-z
    DOI: 10.1007/s10479-005-2456-z
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    References listed on IDEAS

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    1. H. Scolnik & N. Echebest & M.T. Guardarucci & M.C. Vacchino, 2002. "Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems," Annals of Operations Research, Springer, vol. 117(1), pages 95-115, November.
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    Cited by:

    1. Williams López & Marcos Raydan, 2016. "An acceleration scheme for Dykstra’s algorithm," Computational Optimization and Applications, Springer, vol. 63(1), pages 29-44, January.

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