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

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.
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

show all references

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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