Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-rank Approximation of a Matrix: Novel Insights, New Progress, and
  Extensions   Low-rank approximation of a matrix by means of random sampling has been
consistently efficient in its empirical studies by many scientists who applied
it with various sparse and structured multipliers, but adequate formal support
for this empirical phenomenon has been missing so far. Our novel insight into
the subject leads to such an elusive formal support and promises significant
acceleration of the known algorithms for some fundamental problems of matrix
computations and data mining and analysis. Our formal results and our numerical
tests are in good accordance with each other. We also outline extensions of
low-rank approximation algorithms and of our progress to the Least Squares
Regression, the Fast Multipole Method, and the Conjugate Gradient algorithms.

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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga