Discretizing manifolds via minimum energy points
نویسندگان
چکیده
An intuitive method for distributing N points on a manifold A ⊂ Rd is to consider minimal s-energy arrangements of points that interact through a power law (Riesz) potential V = 1/r, where s > 0 and r is Euclidean distance in R 0 . Under what conditions will these points be “uniformly” distributed on A for large N? In this talk I will present recent results characterizing asymptotic properties of s-energy optimal N -point configurations for a class of rectifiable d-dimensional manifold and s ≥ d. Our proofs rely on multiresolution techniques. This is joint work with E. B. Saff.
منابع مشابه
Discretizing Manifolds via Minimum Energy Points, Volume 51, Number 10
1186 NOTICES OF THE AMS VOLUME 51, NUMBER 10 T here are a variety of needs for the discretization of a manifold—statistical sampling, quadrature rules, starting points for Newton’s method, computeraided design, interpolation schemes, finite element tessellations—to name but a few. So let us assume we are given a d-dimensional manifold A in the Euclidean space Rd and wish to determine, say, 5,00...
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