The Euclidean Distance Degree of an Algebraic Variety
نویسندگان
چکیده
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. AMS subject classification: 51N35, 14N10, 14M12, 90C26, 13P25.
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ورودعنوان ژورنال:
- Foundations of Computational Mathematics
دوره 16 شماره
صفحات -
تاریخ انتشار 2016