Resumen de Fitting a Sobolev function to data I

Charles L. Fefferman , Arie Israel, Garving K. Luli

• In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let m≥1 and p>n≥1. Given a finite set E⊂Rn and a function f:E→R, compute an extension F of f belonging to the Sobolev space Wm,p(Rn) 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 CNlogN, where N denotes the cardinality of E, and C depends only on m, n, and p.