The Euclidean Distance Degree of Fermat Hypersurfaces

The Euclidean Distance Degree of Fermat Hypersurfaces

Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a piecewise polynomial whose pieces are defined by subtle congru...

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Veröffentlicht in:arXiv.org 2015-10
1. Verfasser: Lee, Hwangrae
Format: Artikel
Sprache:eng
Schlagworte:
Euclidean geometry
Hyperspaces
Optimization
Polynomials
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Zusammenfassung:Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a piecewise polynomial whose pieces are defined by subtle congruence conditons.
ISSN:2331-8422