JournalsrmiVol. 32, No. 3pp. 1039–1126

Fitting a Sobolev function to data III

  • Charles Fefferman

    Princeton University, United States
  • Arie Israel

    University of Texas at Austin, USA
  • Garving K. Luli

    University of California at Davis, USA
Fitting a Sobolev function to data III cover
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Abstract

In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let m1\mathfrak m \geq 1 and p>n1\mathfrak p > \mathfrak n \geq 1. Given a finite set E Rn\subset \mathbb{R}^\mathfrak n and a function f: E R\rightarrow \mathbb{R}, compute an extension F of f belonging to the Sobolev space Wm,p(Rn)^{\mathfrak m,\mathfrak p}(\mathbb{R}^\mathfrak n) 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 CN log N, where N denotes the cardinality of E, and C depends only on m\mathfrak m, n\mathfrak n, and p\mathfrak p.

Cite this article

Charles Fefferman, Arie Israel, Garving K. Luli, Fitting a Sobolev function to data III. Rev. Mat. Iberoam. 32 (2016), no. 3, pp. 1039–1126

DOI 10.4171/RMI/908