Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Multivariate Fast Discrete Walsh Transform with an Application to
  Function Interpolation   For high dimensional problems, such as approximation and integration, one
cannot afford to sample on a grid because of the curse of dimensionality. An
attractive alternative is to sample on a low discrepancy set, such as an
integration lattice or a digital net. This article introduces a multivariate
fast discrete Walsh transform for data sampled on a digital net that requires
only $O(N \log N)$ operations, where $N$ is the number of data points. This
algorithm and its inverse are digital analogs of multivariate fast Fourier
transforms.
  This fast discrete Walsh transform and its inverse may be used to approximate
the Walsh coefficients of a function and then construct a spline interpolant of
the function. This interpolant may then be used to estimate the function's
effective dimension, an important concept in the theory of numerical
multivariate integration. Numerical results for various functions are
presented.

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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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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: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci