Upper and lower bounds linear in the order for the number of critical points of Hermitian distance minimization on binary forms, with all possible values determined for order three.
The Hermitian Distance degree of an Algebraic Variety
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abstract
In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree introduced in arXiv:1309.0049, replacing a positive symmetric bilinear form by a Hermitian form. Various examples are presented to show the robustness of the machinery.
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The Hermitian Distance degree of Tensor spaces
Upper and lower bounds linear in the order for the number of critical points of Hermitian distance minimization on binary forms, with all possible values determined for order three.