Nearest points on toric varieties

Martin Helmer; Bernd Sturmfels

doi:10.7146/math.scand.a-101478

Nearest points on toric varieties

Martin Helmer, Bernd Sturmfels

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

11 Citationer (Scopus)

Abstract

We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.

Originalsprog	Engelsk
Tidsskrift	Mathematica Scandinavica
Vol/bind	122
Udgave nummer	2
Sider (fra-til)	213-238
Antal sider	26
ISSN	0025-5521
DOI	https://doi.org/10.7146/math.scand.a-101478
Status	Udgivet - 1 jan. 2018

Adgang til dokumentet

10.7146/math.scand.a-101478

http://Nearest Points on Toric VarietiesLicens: Andet

Andre filer og links

Link to publication in Scopus

Citationsformater

@article{47a49931ab5f40ea98ac30cccba3c7be,

title = "Nearest points on toric varieties",

abstract = "We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.",

author = "Martin Helmer and Bernd Sturmfels",

year = "2018",

month = jan,

day = "1",

doi = "10.7146/math.scand.a-101478",

language = "English",

volume = "122",

pages = "213--238",

journal = "Mathematica Scandinavica",

issn = "0025-5521",

publisher = "Aarhus Universitet * Mathematica Scandinavica",

number = "2",

}

TY - JOUR

T1 - Nearest points on toric varieties

AU - Helmer, Martin

AU - Sturmfels, Bernd

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.

AB - We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.

UR - http://www.scopus.com/inward/record.url?scp=85046644168&partnerID=8YFLogxK

U2 - 10.7146/math.scand.a-101478

DO - 10.7146/math.scand.a-101478

M3 - Journal article

AN - SCOPUS:85046644168

SN - 0025-5521

VL - 122

SP - 213

EP - 238

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

IS - 2

ER -