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Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems

Author

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  • H. Scolnik
  • N. Echebest
  • M.T. Guardarucci
  • M.C. Vacchino

Abstract

The Projected Aggregation methods generate the new point x k+1 as the projection of x k onto an “aggregate” hyperplane usually arising from linear combinations of the hyperplanes defined by the blocks. The aim of this paper is to improve the speed of convergence of a particular kind of them by projecting the directions given by the blocks onto the aggregate hyperplane defined in the last iteration. For that purpose we apply the scheme introduced in “A new method for solving large sparse systems of linear equations using row projections” [11], for a given block projection algorithm, to some new methods here introduced whose main features are related to the fact that the projections do not need to be accurately computed. Adaptative splitting schemes are applied which take into account the structure and conditioning of the matrix. It is proved that these new highly parallel algorithms improve the original convergence rate and present numerical results which show their computational efficiency. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:117:y:2002:i:1:p:95-115:10.1023/a:1021565305371
    DOI: 10.1023/A:1021565305371
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    Cited by:

    1. 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.

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