Abstract
We consider the piecewise linear approximation of saddle functions of the form \(f(x,y)=ax^2-by^2\) under the \(L_{\infty }\) error norm. We show that interpolating approximations are not optimal. One can get slightly smaller errors by allowing the vertices of the approximation to move away from the graph of the function.
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Dror Atariah and Günter Rote were supported by Deutsche Forschungsgemeinschaft (DFG) within the DFG Collaborative Research Center TRR 109 Discretization in Geometry and Dynamics. Mathijs Wintraecken was supported by the Future and Emerging Technologies (FET) program within the Seventh Framework Program for Research of the European Commission, under FET-Open Grant Number 255827, as part of the project Computational Geometric Learning. Partial support has been provided by the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions).
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Atariah, D., Rote, G. & Wintraecken, M. Optimal triangulation of saddle surfaces. Beitr Algebra Geom 59, 113–126 (2018). https://doi.org/10.1007/s13366-017-0351-9
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DOI: https://doi.org/10.1007/s13366-017-0351-9