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- W4313294041 abstract "In this note, we recall the study of the Euclidean distance degree of an algebraic set X which is the zero-point set of a polynomial (see [BSW]). Specifically, consider a hypersurface defined by a general polynomial f with its support and contains the origin i.e 0 support of f. In the paper [BSW], the authors study about the Euclidean distance degree (EDD) and found that the EDD of this hypersurface is approximately by the mixed volume (MV) of some Newton polytopes. The main purpose of this note is to study the case that the manifold is defined by two polynomials . We show that the Euclidean distance degree is equal to the solution of the Lagrange multiplier equation. Furthermore, we also find out that the EDD of this variety is not greater than the mixed volume of Newton polytopes of the associated Lagrange multiplier equations." @default.
- W4313294041 created "2023-01-06" @default.
- W4313294041 creator A5034002283 @default.
- W4313294041 date "2022-12-28" @default.
- W4313294041 modified "2023-10-07" @default.
- W4313294041 title "Euclidean distance degree of zero-set of two polynomials" @default.
- W4313294041 doi "https://doi.org/10.56764/hpu2.jos.2022.1.2.68-75" @default.
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