Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear tensor product approximation of functions   We are interested in approximation of a multivariate function
$f(x_1,\dots,x_d)$ by linear combinations of products $u^1(x_1)\cdots u^d(x_d)$
of univariate functions $u^i(x_i)$, $i=1,\dots,d$. In the case $d=2$ it is a
classical problem of bilinear approximation. In the case of approximation in
the $L_2$ space the bilinear approximation problem is closely related to the
problem of singular value decomposition (also called Schmidt expansion) of the
corresponding integral operator with the kernel $f(x_1,x_2)$. There are known
results on the rate of decay of errors of best bilinear approximation in $L_p$
under different smoothness assumptions on $f$. The problem of multilinear
approximation (nonlinear tensor product approximation) in the case $d\ge 3$ is
more difficult and much less studied than the bilinear approximation problem.
We will present results on best multilinear approximation in $L_p$ under mixed
smoothness assumption on $f$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th