Fitting a Sobolev function to data III

TY - JOUR

T1 - Fitting a Sobolev function to data III

AU - Fefferman, Charles

AU - Israel, Arie

AU - Luli, Garving K.

N1 - Funding Information: Charles Fefferman's research is supported by NSF grant DMS-1265524 and AFOSR grant FA9550-12-1-0425. Publisher Copyright: © 2016 European Mathematical Society.

PY - 2016

Y1 - 2016

N2 - In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let m ≥ 1 and p > n ≥ 1. Given a finite set E C Rn and a function f : E → R, compute an extension F of f belonging to the Sobolev space Wm,p(Rn) with norm having the smallest possible order of magnitude; secondly, compute the order of magnitude of the norm of F. The combined running time of our algorithms is at most CNlogN, where N denotes the cardinality of E, and C depends only on m, n, and p.

AB - In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let m ≥ 1 and p > n ≥ 1. Given a finite set E C Rn and a function f : E → R, compute an extension F of f belonging to the Sobolev space Wm,p(Rn) with norm having the smallest possible order of magnitude; secondly, compute the order of magnitude of the norm of F. The combined running time of our algorithms is at most CNlogN, where N denotes the cardinality of E, and C depends only on m, n, and p.

KW - Algorithm

KW - Interpolation

KW - Sobolev spaces

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U2 - 10.4171/rmi/908

DO - 10.4171/rmi/908

M3 - Article

SN - 0213-2230

VL - 32

SP - 1039

EP - 1126

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 3

ER -