Kaczmarz algorithm in Hilbert space

Volume 169 / 2005

Rainis Haller, Ryszard Szwarc Studia Mathematica 169 (2005), 123-132 MSC: Primary 41A65. DOI: 10.4064/sm169-2-2


The aim of the Kaczmarz algorithm is to reconstruct an element in a Hilbert space from data given by inner products of this element with a given sequence of vectors. The main result characterizes sequences of vectors leading to reconstruction of any element in the space. This generalizes some results of Kwapień and Mycielski.


  • Rainis HallerInstitute of Pure Mathematics
    Faculty of Mathematics and Computer Science
    University of Tartu
    Ülikooli 18
    50090 Tartu, Estonia
  • Ryszard SzwarcInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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