Papers › Computing minimal interpolants in C^(1,1)(ℝᵈ)
Computing minimal interpolants in C^(1,1)(ℝᵈ)
Ariel Herbert-Voss, Matthew J. Hirn, Frederick McCollum
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We consider the following interpolation problem. Suppose one is given a finite set E ⊂ℝᵈ, a function f: E →ℝ, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈C^(1,1)(ℝᵈ) with the minimum possible value of Lip (∇F). We present practical, efficient algorithms for constructing an F such that Lip (∇F) is minimal, or for less computational effort, within a small dimensionless constant of being minimal.
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