On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
نویسندگان
چکیده
منابع مشابه
Minimum Volume Enclosing Ellipsoids
Two different methods for computing the covering ellipses of a set of points are presented. The first method finds the optimal ellipsoids with the minimum volume. The second method uses the first and second moments of the data points to compute the parameters of an ellipsoid that covers most of the points. A MATLAB software is written to verify the results.
متن کاملOn Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Given A := {a1, . . . , am} ⊂ Rd whose affine hull is Rd, we study the problems of computing an approximate rounding of the convex hull of A and an approximation to the minimum volume enclosing ellipsoid of A. In the case of centrally symmetric sets, we first establish that Khachiyan’s barycentric coordinate descent (BCD) method is exactly the polar of the deepest cut ellipsoid method using two...
متن کاملMinimum Volume Enclosing Ellipsoids and Core Sets
Abstract. We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p1, p2, . . . , pn} ⊆ Rd. Based on a simple, initial volume approximation method, we propose a modification of Khachiyan’s first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd3/ ) operations for ∈ (0, 1). As a byproduct, our ...
متن کاملMinimum-Volume Enclosing Ellipsoids and Core Sets1
We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p, p, . . . , p} ⊆ R. Based on a simple, initial volume approximation method, we propose a modification of Khachiyan’s first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd/ ) operations for ∈ (0, 1). As a byproduct, our algorithm retur...
متن کاملComputing Minimum-Volume Enclosing Axis-Aligned Ellipsoids
Given a set of points S = {x1, . . . , xm} ⊂ R and > 0, we propose and analyze an algorithm for the problem of computing a (1 + )-approximation to the minimum-volume axis-aligned ellipsoid enclosing S . We establish that our algorithm is polynomial for fixed . In addition, the algorithm returns a small core set X ⊆ S , whose size is independent of the number of points m, with the property that ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2007
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.02.013