JournalsrmiVol. 32, No. 2pp. 649–750

Fitting a Sobolev function to data II

  • 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 II 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)W^{\mathfrak {m,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 II. Rev. Mat. Iberoam. 32 (2016), no. 2, pp. 649–750

DOI 10.4171/RMI/897