Fitting a Cm-smooth function to data I

• 成果类型: Article
• 署名作者: Fefferman, Charles; Klartag, Bo'az
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.315
• 发表日期: 2009
• 页码: 315-346
• 关键词: whitneys extension problem; closed-sets; linear-operators; THEOREM

摘要

Suppose we are given a finite subset E subset of R-n and a function f : E -> R. How to extend f to a C-m function F : R-n -> R with C-m norm of the smallest possible order of magnitude? In this paper and in [20] we tackle this question from the perspective of theoretical computer science. We exhibit algorithms for constructing such an extension function F, and for computing the order of magnitude of its C-m norm. The running time of our algorithms is never more than CN log N, where N is the cardinality of E and C is a constant depending only on m and n.