Full length articleSet-valued Hermite interpolation☆
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Highlights
► Directed sets are a tool to visualize (non-convex) differences of embedded convex compacts. ► Derivatives of set-valued maps are calculated in the Banach space of directed sets. ► Hermite interpolation extends known linear interpolation for convex-valued maps. ► Convergence results from the real-valued case carry over to the set-valued framework. ► Numerical interpolation based on support functions and points delivers good results.
Keywords
Set-valued interpolation
Hermite interpolation
Embedding of convex, compact sets
Directed sets
Derivatives of set-valued maps
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This work was partially supported by the Hausdorff Research Institute for Mathematics, Bonn, within the HIM Junior Semester Program “Computational Mathematics” in February–April 2008.
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