TY - JOUR
T1 - Efficient Algorithms for Approximate Smooth Selection
AU - Fefferman, Charles
AU - Guillén Pegueroles, Bernat
N1 - Publisher Copyright:
© 2019, Mathematica Josephina, Inc.
PY - 2021/7
Y1 - 2021/7
N2 - In this paper, we provide efficient algorithms for approximate Cm(Rn, RD) - selection. In particular, given a set E, a constant M> 0 , and convex sets K(x) ⊂ RD for x∈ E, we show that an algorithm running in C(τ) Nlog N steps is able to solve the smooth selection problem of selecting a point y∈ (1 + τ) ⧫K(x) for x∈ E for an appropriate dilation of K(x), (1 + τ) ⧫K(x) , and guaranteeing that a function interpolating the points (x, y) will be Cm(Rn, RD) with norm bounded by CM.
AB - In this paper, we provide efficient algorithms for approximate Cm(Rn, RD) - selection. In particular, given a set E, a constant M> 0 , and convex sets K(x) ⊂ RD for x∈ E, we show that an algorithm running in C(τ) Nlog N steps is able to solve the smooth selection problem of selecting a point y∈ (1 + τ) ⧫K(x) for x∈ E for an appropriate dilation of K(x), (1 + τ) ⧫K(x) , and guaranteeing that a function interpolating the points (x, y) will be Cm(Rn, RD) with norm bounded by CM.
KW - Approximate algorithms
KW - Efficient algorithms
KW - Partition of unity
KW - Smooth selection
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U2 - 10.1007/s12220-019-00242-y
DO - 10.1007/s12220-019-00242-y
M3 - Article
AN - SCOPUS:85070688993
SN - 1050-6926
VL - 31
SP - 6530
EP - 6600
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 7
ER -