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Efficient Algorithms for Approximate Smooth Selection | Charles Fefferman
; Bernat Guillen Pegueroles
; | Date: |
8 May 2019 | Abstract: | In this paper we provide efficient algorithms for approximate
$mathcal{C}^m(mathbb{R}^n, mathbb{R}^D)-$selection. In particular, given a
set $E$, constants $M_0 > 0$ and $0 < au leq au_{max}$, and convex sets
$K(x) subset mathbb{R}^D$ for $x in E$, we show that an algorithm running in
$C( au) N log N$ steps is able to solve the smooth selection problem of
selecting a point $y in (1+ au)lacklozenge K(x)$ for $x in E$ for an
appropriate dilation of $K(x)$, $(1+ au)lacklozenge K(x)$, and guaranteeing
that a function interpolating the points $(x, y)$ will be
$mathcal{C}^m(mathbb{R}^n, mathbb{R}^D)$ with norm bounded by $C M_0$. | Source: | arXiv, 1905.4156 | Services: | Forum | Review | PDF | Favorites |
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