Semidefinite Representation of the K-ellipse
نویسندگان
چکیده
The k-ellipse is the plane algebraic curve consisting of all points whose sum of distances from k given points is a fixed number. The polynomial equation defining the k-ellipse has degree 2k if k is odd and degree 2k− ` k k/2 ́ if k is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted k-ellipses and k-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.
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