Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjecture of error boundedness in a new Hermite interpolation problem
  via splines of odd-degree   We present a Hermite interpolation problem via splines of odd-degree which,
to the best knowledge of the authors, has not been considered in the literature
on interpolation via odd-degree splines. In this new interpolation problem, we
conjecture that the interpolation error is bounded in the supremum norm
independently of the locations of the knots. Given an integer k greater than or
equal to 3, our spline interpolant is of degree 2k-1 and with 2k-4 (interior)
knots. Simulations were performed to check the validity of the conjecture. We
present strong numerical evidence in support of the conjecture for k=3, ..., 10
when the interpolated function belongs to C^{(2k)}[0,1], the class of 2k-times
continuously differentiable functions on [0,1]. In this case, the worst
interpolation error is proved to be attained by the perfect spline of degree 2k
with the same knots as the spline interpolant. This interpolation problem
arises naturally in nonparametric estimation of a multiply monotone density via
Least Squares and Maximum Likehood methods.

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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex