We study the relaxed Kaczmarz algorithm in Hilbert space. The connection with the non-relaxed algorithm is examined. In particular we give sufficient conditions when relaxation leads to the convergence of the algorithm independently of the relaxation coefficients.
@article{10_4064_sm216_3_3,
author = {Ryszard Szwarc and Grzegorz \'Swiderski},
title = {Kaczmarz algorithm with relaxation in {Hilbert} space},
journal = {Studia Mathematica},
pages = {237--243},
year = {2013},
volume = {216},
number = {3},
doi = {10.4064/sm216-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm216-3-3/}
}
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AU - Ryszard Szwarc
AU - Grzegorz Świderski
TI - Kaczmarz algorithm with relaxation in Hilbert space
JO - Studia Mathematica
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SP - 237
EP - 243
VL - 216
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Ryszard Szwarc; Grzegorz Świderski. Kaczmarz algorithm with relaxation in Hilbert space. Studia Mathematica, Tome 216 (2013) no. 3, pp. 237-243. doi: 10.4064/sm216-3-3