Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Successive Coordinate Search and Component-by-Component Construction of
  Rank-1 Lattice Rules   The (fast) component-by-component (CBC) algorithm is an efficient tool for
the construction of generating vectors for quasi-Monte Carlo rank-1 lattice
rules in weighted reproducing kernel Hilbert spaces. We consider product
weights, which assigns a weight to each dimension. These weights encode the
effect a certain variable (or a group of variables by the product of the
individual weights) has. Smaller weights indicate less importance. Kuo (2003)
proved that the CBC algorithm achieves the optimal rate of convergence in the
respective function spaces, but this does not imply the algorithm will find the
generating vector with the smallest worst-case error. In fact it does not. We
investigate a generalization of the component-by-component construction that
allows for a general successive coordinate search (SCS), based on an initial
generating vector, and with the aim of getting closer to the smallest
worst-case error. The proposed method admits the same type of worst-case error
bounds as the CBC algorithm, independent of the choice of the initial vector.
Under the same summability conditions on the weights as in [Kuo,2003] the error
bound of the algorithm can be made independent of the dimension $d$ and we
achieve the same optimal order of convergence for the function spaces from
[Kuo,2003]. Moreover, a fast version of our method, based on the fast CBC
algorithm by Nuyens and Cools, is available, reducing the computational cost of
the algorithm to $O(d \, n \log(n))$ operations, where $n$ denotes the number
of function evaluations. Numerical experiments seeded by a Korobov-type
generating vector show that the new SCS algorithm will find better choices than
the CBC algorithm and the effect is better when the weights decay slower.

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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: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th