Interpolation by linear programming I

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May 2011, 30(2): 477-492. doi: 10.3934/dcds.2011.30.477

Interpolation by linear programming I

1.	Department of Mathematics, Princeton University, 1102 Fine Hall, Washington Road, Princeton, New Jersey 08544, United States

Received May 2010 Published February 2011

Abstract
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Given $m , n \geq 2$ and $\epsilon > 0$, we compute a function taking prescribed values at $N$ given points of $\mathbb{R}^n$, and having $C^m$ norm as small as possible up to a factor $1 + \epsilon$. Our computation reduces matters to a linear programming problem.

Keywords: Interpolation, linear programming..

Mathematics Subject Classification: 65D05, 65D1.

Citation: Charles Fefferman. Interpolation by linear programming I. Discrete & Continuous Dynamical Systems - A, 2011, 30 (2) : 477-492. doi: 10.3934/dcds.2011.30.477

References:

[1]	C. Fefferman, The $C^m$ norm of a function with prescribed jets II,, Revista Mathem\'atica Iberoamericana, 25 (2009), 275. Google Scholar
[2]	C. Fefferman, "Interpolation by Linear Programming II,'', (to appear)., (). Google Scholar
[3]	E. LeGruyer, Minimal Lipschitz extensions to differentiable functions defined on a Hilbert space,, {Geometric and Functional Analysis}, 19 (2009), 1101. doi: 10.1007/s00039-009-0027-1. Google Scholar

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References:

[1]	C. Fefferman, The $C^m$ norm of a function with prescribed jets II,, Revista Mathem\'atica Iberoamericana, 25 (2009), 275. Google Scholar
[2]	C. Fefferman, "Interpolation by Linear Programming II,'', (to appear)., (). Google Scholar
[3]	E. LeGruyer, Minimal Lipschitz extensions to differentiable functions defined on a Hilbert space,, {Geometric and Functional Analysis}, 19 (2009), 1101. doi: 10.1007/s00039-009-0027-1. Google Scholar

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