Numerically intersecting algebraic varieties via witness sets
نویسندگان
چکیده
The fundamental construct of numerical algebraic geometry is the representation of an irreducible algebraic set, A, by a witness set, which consists of a polynomial system, F , for which A is an irreducible component of V(F ), a generic linear space L of complementary dimension to A, and a numerical approximation to the set of witness points, L ∩A. Given F , methods exist for computing a numerical irreducible decomposition, which consists of a collection of witness sets, one for each irreducible component of V(F ). This paper concerns the more refined question of finding a numerical irreducible decomposition of the intersection A ∩B of two irreducible algebraic sets, A and B, given a witness set for each. An existing algorithm, the diagonal homotopy, computes witness point supersets for A ∩ B, but this does not complete the numerical irreducible decomposition. In this paper, we use the theory of isosingular sets to complete the process of computing the numerical irreducible decomposition of the intersection.
منابع مشابه
Publications of Charles W. Wampler Edited Books
Decoupled torque control of tendon-driven fingers with tension management, " Int. Numerically intersecting algebraic varieties via witness sets, " Applied Math.
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ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 219 شماره
صفحات -
تاریخ انتشار 2013