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Euclidean Distance Degree and Mixed Volume [PDF]
Foundations of Computational Mathematics, 2021 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 ...
Breiding, P., Sottile, F., Woodcock, J.
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Euclidean Distance Degree of the Multiview Variety [PDF]
SIAM Journal on Applied Algebra and Geometry, 2020 Euclidean distance degree, multiview variety, triangulation problem, non-proper Morse theory, Euler-Poincare characteristic, local Euler ...
Laurentiu Maxim, Botong Wang
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The Euclidean Distance Degree of an Algebraic Variety [PDF]
Foundations of Computational Mathematics, 2015 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.
Jan Draisma +2 more
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Defect of Euclidean distance degree
Advances in Applied Mathematics, 2020 Two well studied invariants of a complex projective variety are the unit Euclidean distance degree and the generic Euclidean distance degree. These numbers give a measure of the algebraic complexity for "nearest" point problems of the algebraic variety. It is well known that the latter is an upper bound for the former.
Laurentiu Maxim +2 more
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The euclidean distance degree of orthogonally invariant matrix varieties [PDF]
Israel Journal of Mathematics, 2017 We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances.
Dmitriy Drusvyatskiy +2 more
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Euclidean Distance Degree in Manifold Optimization
SIAM Journal on Optimization14 ...
Lek-Heng Lim, Ke Ye
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The Euclidean distance degree of Fermat hypersurfaces
Journal of Symbolic Computation, 2017 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.
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Approximating Euclidean distances by small degree graphs [PDF]
Discrete and Computational Geometry, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finding Optimal Stations Using Euclidean Distance and Adjustable Surrounding Sphere
Applied Sciences, 2021 Air quality monitoring network (AQMN) plays an important role in air pollution management. However, setting up an initial network in a city often lacks necessary information such as historical pollution and geographical data, which makes it challenging ...
Athita Onuean +2 more
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IEEE Access, 2023 The notion of a complex hesitant fuzzy set (CHFS) is one of the better tools in order to deal with complex information. Since distance plays a crucial role in order to differentiate between two things or sets, in this paper, we first develop a priority ...
Muhammad Sajjad Ali Khan +4 more
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