Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Bibliography submission using bibtex file | Links | Help | Internal


TitleMetric problems for quadrics in multidimensional space
Author(s) A. Yu. Uteshev, Marina V. Yashina
TypeArticle in Journal
AbstractAbstract Given the equations of the first and the second order manifolds in R n , we construct the distance equation, i.e. a univariate algebraic equation one of the zeros of which (generically minimal positive) coincides with the square of the distance between these manifolds. To achieve this goal we employ Elimination Theory methods. In the frame of this approach we also deduce the necessary and sufficient algebraic conditions under which the manifolds intersect and propose an algorithm for finding the coordinates of their nearest points. The case of parameter dependent manifolds is also considered.
KeywordsEllipsoid, Quadric, Distance, Intersection of algebraic manifolds
URL http://www.sciencedirect.com/science/article/pii/S0747717114000893
JournalJournal of Symbolic Computation
Volume68, Part 1
Pages287 - 315
Translation No
Refereed No