The Jet of an Interpolant on a Finite Set

Charles Fefferman; Arie Israel

doi:10.4171/RMI/639

The Jet of an Interpolant on a Finite Set

Charles Fefferman, Arie Israel

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study functions F ε C^m(ℝⁿ) having norm less than a given constant M, and agreeing with a given function f on a finite set E. Let Γ_f(S, M) denote the convex set formed by taking the (m- 1 )jets of all such F at a given finite set S ⊂ ℝⁿ. We provide an efficient algorithm to compute a convex polyhedron Γ_f(S, M), such that Γ_f(S, cM) ⊂ Γ_f(S, M) ⊂ Γ_f(S, CM), where c and C depend only on m and n.

Original language	English (US)
Pages (from-to)	355-360
Number of pages	6
Journal	Revista Matematica Iberoamericana
Volume	27
Issue number	1
DOIs	https://doi.org/10.4171/RMI/639
State	Published - 2011

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

Algorithm
Interpolation
Jet
Whitney extension theorem

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abstract = "We study functions F ε Cm(ℝn) having norm less than a given constant M, and agreeing with a given function f on a finite set E. Let Γf(S, M) denote the convex set formed by taking the (m- 1 )jets of all such F at a given finite set S ⊂ ℝn. We provide an efficient algorithm to compute a convex polyhedron Γf(S, M), such that Γf(S, cM) ⊂ Γf(S, M) ⊂ Γf(S, CM), where c and C depend only on m and n.",

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AU - Israel, Arie

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N2 - We study functions F ε Cm(ℝn) having norm less than a given constant M, and agreeing with a given function f on a finite set E. Let Γf(S, M) denote the convex set formed by taking the (m- 1 )jets of all such F at a given finite set S ⊂ ℝn. We provide an efficient algorithm to compute a convex polyhedron Γf(S, M), such that Γf(S, cM) ⊂ Γf(S, M) ⊂ Γf(S, CM), where c and C depend only on m and n.

AB - We study functions F ε Cm(ℝn) having norm less than a given constant M, and agreeing with a given function f on a finite set E. Let Γf(S, M) denote the convex set formed by taking the (m- 1 )jets of all such F at a given finite set S ⊂ ℝn. We provide an efficient algorithm to compute a convex polyhedron Γf(S, M), such that Γf(S, cM) ⊂ Γf(S, M) ⊂ Γf(S, CM), where c and C depend only on m and n.

KW - Algorithm

KW - Interpolation

KW - Jet

KW - Whitney extension theorem

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The Jet of an Interpolant on a Finite Set

Abstract

All Science Journal Classification (ASJC) codes

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