Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Literature survey on low rank approximation of matrices   Low rank approximation of matrices has been well studied in literature.
Singular value decomposition, QR decomposition with column pivoting, rank
revealing QR factorization (RRQR), Interpolative decomposition etc are
classical deterministic algorithms for low rank approximation. But these
techniques are very expensive $(O(n^{3})$ operations are required for $n\times
n$ matrices). There are several randomized algorithms available in the
literature which are not so expensive as the classical techniques (but the
complexity is not linear in n). So, it is very expensive to construct the low
rank approximation of a matrix if the dimension of the matrix is very large.
There are alternative techniques like Cross/Skeleton approximation which gives
the low-rank approximation with linear complexity in n . In this article we
review low rank approximation techniques briefly and give extensive references
of many techniques.

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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom