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. 275–376DOI 10.4171/RMI/887