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Title: On the Denominator of Wachspress Basis Functions for Polycons of Order Six
Authors: Wachspress, Jacob
Advisors: Kollar, Janos
Department: Mathematics
Class Year: 2020
Abstract: Eugene Wachspress's (1975) rational basis functions allow function approximation over regions bounded by lines and conics, called polycons [1]. 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 [1] 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
Language: en
Appears in Collections:Mathematics, 1934-2020

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