Fitting a Sobolev function to data I

  • Charles Fefferman

    Princeton University, United States
  • Arie Israel

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

    University of California at Davis, USA

Abstract

In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let and . Given a finite set and a function , compute an extension of belonging to the Sobolev space with norm having the smallest possible order of magnitude; secondly, compute the order of magnitude of the norm of . The combined running time of our algorithms is at most , where denotes the cardinality of , and depends only on , , and .

Cite this article

Charles Fefferman, Arie Israel, Garving K. Luli, Fitting a Sobolev function to data I. Rev. Mat. Iberoam. 32 (2016), no. 1, pp. 275–376

DOI 10.4171/RMI/887