Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note On The Randomized Kaczmarz Method With A Partially Weighted
  Selection Step   In this note we reconsider two known algorithms which both usually converge
faster than the randomized Kaczmarz method introduced by Strohmer and
Vershynin(2009), but require the additional computation of all residuals of an
iteration at each step. As already indicated in the literature, e.g.
arXiv:2007.02910 and arXiv:2011.14693, it is shown that the non-randomized
version of the two algorithms converges at least as fast as the randomized
version, while still requiring computation of all residuals. Based on that
observation, a new simple random sample selection scheme has been introduced by
arXiv:2011.14693 to reduce the required total of residuals. In the same light
we propose an alternative random selection scheme which can easily be included
as a `partially weighted selection step' into the classical randomized Kaczmarz
algorithm without much ado. Numerical examples show that the randomly
determined number of required residuals can be quite moderate.

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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys