Interpolation by linear programming I

Charles Fefferman

doi:10.3934/dcds.2011.30.477

Article Contents

2011, Volume 30, Issue 2: 477-492. Doi: 10.3934/dcds.2011.30.477 open access

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Interpolation by linear programming I

Charles Fefferman^1,

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

Received: April 30, 2010

Published: May 2011

Abstract Related Papers Cited by

Abstract

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

Keywords:

Interpolation,
linear programming.

Mathematics Subject Classification: 65D05, 65D17.

Citation:

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References

[1]	C. Fefferman, The $C^m$ norm of a function with prescribed jets II, Revista Mathemática Iberoamericana, 25 (2009), 275-421.
[2]	C. Fefferman, "Interpolation by Linear Programming II,'' (to appear).
[3]	E. LeGruyer, Minimal Lipschitz extensions to differentiable functions defined on a Hilbert space, Geometric and Functional Analysis, 19 (2009), 1101-1118.doi: 10.1007/s00039-009-0027-1.