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

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Ovidius University, Blvd. Mamaia 124, 8700, Constanta, Romania

    Constantin Popa

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  1. Constantin Popa
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Correspondence to Constantin Popa.

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Popa, C. Characterization of the solutions set of inconsistent least-squares problems by an extended Kaczmarz algorithm. Korean J. Comput. & Appl. Math. 6, 51–64 (1999). https://doi.org/10.1007/BF02941906

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  • DOI: https://doi.org/10.1007/BF02941906

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