Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subspace Iteration Randomization and Singular Value Problems   A classical problem in matrix computations is the efficient and reliable
approximation of a given matrix by a matrix of lower rank. The truncated
singular value decomposition (SVD) is known to provide the best such
approximation for any given fixed rank. However, the SVD is also known to be
very costly to compute. Among the different approaches in the literature for
computing low-rank approximations, randomized algorithms have attracted
researchers' recent attention due to their surprising reliability and
computational efficiency in different application areas. Typically, such
algorithms are shown to compute with very high probability low-rank
approximations that are within a constant factor from optimal, and are known to
perform even better in many practical situations. In this paper, we present a
novel error analysis that considers randomized algorithms within the subspace
iteration framework and show with very high probability that highly accurate
low-rank approximations as well as singular values can indeed be computed
quickly for matrices with rapidly decaying singular values. Such matrices
appear frequently in diverse application areas such as data analysis, fast
structured matrix computations and fast direct methods for large sparse linear
systems of equations and are the driving motivation for randomized methods.
Furthermore, we show that the low-rank approximations computed by these
randomized algorithms are actually rank-revealing approximations, and the
special case of a rank-1 approximation can also be used to correctly estimate
matrix 2-norms with very high probability. Our numerical experiments are in
full support of our conclusions.

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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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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: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex