Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Several Approaches to Break the Curse of Dimensionality   In modern science the efficient numerical treatment of high-dimensional
problems becomes more and more important. A fundamental insight of the theory
of information-based complexity (IBC for short) is that the computational
hardness of a problem can not be described properly only by the rate of
convergence. There exist problems for which an exponential number of
information operations is needed in order to reduce the initial error, although
there are algorithms which provide an arbitrary large rate of convergence.
Problems that yield this exponential dependence are said to suffer from the
curse of dimensionality. While analyzing numerical problems it turns out that
we can often vanquish this curse by exploiting additional structural
properties. The aim of this thesis is to present several approaches of this
type. Moreover, a detailed introduction to the field of IBC is given.

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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: acc-phys