Euclidean distance degree and mixed volume Institutional Repository Document uri icon

abstract

  • We initiate a study of the Euclidean Distance Degree in the context of sparse polynomials. Specifically, we consider a hypersurface 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 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.

author list (cited authors)

  • Breiding, P., Sottile, F., & Woodcock, J.

citation count

  • 0

complete list of authors

  • Breiding, Paul||Sottile, Frank||Woodcock, James

Book Title

  • arXiv

publication date

  • December 2020