In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let and . Given a finite set E and a function f: E , compute an extension F of f belonging to the Sobolev space W 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 , , and .
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. 1039–1126DOI 10.4171/RMI/908