Euclidean distance degrees of real algebraic groups
نویسندگان
چکیده
Article history: Received 22 May 2014 Accepted 8 November 2014 Available online 25 November 2014 Submitted by J.M. Landsberg MSC: 15B99 13P25 20G20
منابع مشابه
On the Quaternionic Curves in the Semi-Euclidean Space E_4_2
In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.
متن کاملThe Euclidean Distance Degree of an Algebraic Variety
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 degre...
متن کاملSilhouette-based 2D-3D Pose Estimation Using Algebraic Surfaces
In this contribution we present a formulation of the 2D3D pose estimation problem using implicit algebraic surfaces. To model the projective mapping, we apply novel Dixon resultant heuristics to deal with the rapidly increasing polynomial degrees of projected image outlines. The advantages as well as disadvantages of using linearised twist coordinates for pose representation are also discussed....
متن کاملNew distance and similarity measures for hesitant fuzzy soft sets
The hesitant fuzzy soft set (HFSS), as a combination of hesitant fuzzy and soft sets, is regarded as a useful tool for dealing with the uncertainty and ambiguity of real-world problems. In HFSSs, each element is defined in terms of several parameters with arbitrary membership degrees. In addition, distance and similarity measures are considered as the important tools in different areas such as ...
متن کاملCounting Real Critical Points of the Distance to Orthogonally Invariant Matrix Sets
Minimizing the Euclidean distance to a set arises frequently in applications. When the set is algebraic, a measure of complexity of this optimization problem is its number of critical points. In this paper we provide a general framework to compute and count the real smooth critical points of a data matrix on an orthogonally invariant set of matrices. The technique relies on “transfer principles...
متن کامل