Characterization of the solutions set of inconsistent least-squares problems by an extended Kaczmarz algorithm



We give a new characterization of the solutions set of the general (inconsistent) linear least-squares problem using the set of limit-points of an extended version of the classical Kaczmarz’s projections method. We also obtain a “ step error reduction formula” which, in some cases, can give us apriori information about the convergence properties of the algorithm. Some numerical experiments with our algorithm and comparisons between it and others existent in the literature, are made in the last section of the paper.

AMS Mathematics Subject Classification

65F10 65F20 

Key word and phrases

least-squares problems extended Kaczmarz algorithm 


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Copyright information

© Korean Society for Computational and Applied Mathematics 1999

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsOvidius UniversityConstantaRomania

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