Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of Krylov Subspace Solutions of Regularized Nonconvex Quadratic
  Problems   We provide convergence rates for Krylov subspace solutions to the
trust-region and cubic-regularized (nonconvex) quadratic problems. Such
solutions may be efficiently computed by the Lanczos method and have long been
used in practice. We prove error bounds of the form $1/t^2$ and
$e^{-4t/\sqrt{\kappa}}$, where $\kappa$ is a condition number for the problem,
and $t$ is the Krylov subspace order (number of Lanczos iterations). We also
provide lower bounds showing that our analysis is sharp.

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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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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: solv-int