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Foundations of Computational Mathematics
Erschienen in: Foundations of Computational Mathematics 1/2016

01.02.2016

The Euclidean Distance Degree of an Algebraic Variety

verfasst von: Jan Draisma, Emil Horobeţ, Giorgio Ottaviani, Bernd Sturmfels, Rekha R. Thomas

Erschienen in: Foundations of Computational Mathematics | Ausgabe 1/2016

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Abstract

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low-rank matrices, the Eckart–Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest point maps from the perspective of computational algebraic geometry. The Euclidean distance degree of a variety is the number of critical points of the squared distance to a general point outside the variety. Focusing on varieties seen in applications, we present numerous tools for exact computations.
Vorheriger Artikel Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
Nächster Artikel Arbitrary-Order Trigonometric Fourier Collocation Methods for Multi-Frequency Oscillatory Systems

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Metadaten
Titel
The Euclidean Distance Degree of an Algebraic Variety
verfasst von
Jan Draisma
Emil Horobeţ
Giorgio Ottaviani
Bernd Sturmfels
Rekha R. Thomas
Publikationsdatum
01.02.2016
Verlag
Springer US
Erschienen in
Foundations of Computational Mathematics / Ausgabe 1/2016
Print ISSN: 1615-3375
Elektronische ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-014-9240-x

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