Levels of nonoptimality of the Weiszfeld Algorithm in the least-modules method

  • Authors:

  • P. A. Akimov;A. I. Matasov

  • Affiliations:

  • Lomonosov State University, Moscow, Russia;Lomonosov State University, Moscow, Russia and Institute of Space Research, Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2010

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Abstract

The least-modules method allows one to process efficiently the data with anomalously great errors. The paper was devoted to the Weiszfeld algorithm enabling one to solve approximately the variational problem corresponding to the least-modules method. Estimates of nonoptimality of the algorithms's iterations enabling one to estimate the quality of the approximate solution with anomalously great errors were obtained on the basis of the duality theory of the convex variational problems.