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|Title:||On the Denominator of Wachspress Basis Functions for Polycons of Order Six|
|Abstract:||Eugene Wachspress's (1975) rational basis functions allow function approximation over regions bounded by lines and conics, called polycons . It is still an open conjecture that the denominator of a Wachspress basis function does not equal zero at any point on the polycon. Proof of this conjecture is necessary to ensure the basis functions are well-defined. In this thesis, we construct the Wachspress basis functions in a more streamlined fashion than  and then explain efforts to prove Wachspress's conjecture for polycons bounded by exactly three conics, the simplest case where a counterexample may occur. We make some progress toward a continuity argument that would allow the problem to be split into finitely many cases and provide MATLAB code to test these cases.|
|Type of Material:||Princeton University Senior Theses|
|Appears in Collections:||Mathematics, 1934-2020|
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