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Single projection Kaczmarz extended algorithms

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An Erratum to this article was published on 14 August 2017

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Abstract

In order to find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, so that a consistent system is asymptotically obtained, and applies Kaczmarz iterations for the current approximation of this system. It has been shown that for random corrections of the right hand side and Kaczmarz updates selected at random, the algorithm converges to the least squares solution. In this work we consider deterministic strategies like the maximal-residual and the almost-cyclic control, and show convergence to a least squares solution.

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  • 14 August 2017

    An erratum to this article has been published.

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Authors and Affiliations

  1. Mathematical Imaging Group, University of Heidelberg, 69115, Heidelberg, Germany

    Stefania Petra

  2. Faculty of Mathematics and Informatics, OVIDIUS University of Constanta, Blvd. Mamaia 124, 900527, Constanţa, Romania

    Constantin Popa

Authors
  1. Stefania Petra
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  2. Constantin Popa
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Correspondence to Constantin Popa.

Additional information

An erratum to this article is available at https://doi.org/10.1007/s11075-017-0390-1.

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Petra, S., Popa, C. Single projection Kaczmarz extended algorithms. Numer Algor 73, 791–806 (2016). https://doi.org/10.1007/s11075-016-0118-7

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  • DOI: https://doi.org/10.1007/s11075-016-0118-7

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