Author:
Breiding P.,Sottile F.,Woodcock J.
Abstract
AbstractWe initiate a study of the Euclidean distance degree in the context of sparse polynomials. Specifically, we consider a hypersurface $$f=0$$
f
=
0
defined by a polynomial f that is general given its support, such that the support contains the origin. We show that the Euclidean distance degree of $$f=0$$
f
=
0
equals the mixed volume of the Newton polytopes of the associated Lagrange multiplier equations. We discuss the implication of our result for computational complexity and give a formula for the Euclidean distance degree when the Newton polytope is a rectangular parallelepiped.
Funder
Max Planck Institute for Mathematics in the Sciences
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Analysis
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