Standard

Metric Problems for Quadrics in Multidimensional Space. / Uteshev, A.Y.; Yashina, M.V.

In: Journal of Symbolic Computation, Vol. 68, No. 1, 2015, p. 287-315.

Research output: Contribution to journal › Article › peer-review

Harvard

Uteshev, AY & Yashina, MV 2015, 'Metric Problems for Quadrics in Multidimensional Space', Journal of Symbolic Computation, vol. 68, no. 1, pp. 287-315. https://doi.org/10.1016/j.jsc.2014.09.021

APA

Uteshev, A. Y., & Yashina, M. V. (2015). Metric Problems for Quadrics in Multidimensional Space. Journal of Symbolic Computation, 68(1), 287-315. https://doi.org/10.1016/j.jsc.2014.09.021

Vancouver

Uteshev AY, Yashina MV. Metric Problems for Quadrics in Multidimensional Space. Journal of Symbolic Computation. 2015;68(1):287-315. https://doi.org/10.1016/j.jsc.2014.09.021

Author

Uteshev, A.Y. ; Yashina, M.V. / Metric Problems for Quadrics in Multidimensional Space. In: Journal of Symbolic Computation. 2015 ; Vol. 68, No. 1. pp. 287-315.

BibTeX

@article{c5bfa74ba9f640f696f050a20452201a,
title = "Metric Problems for Quadrics in Multidimensional Space",
abstract = "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.",
keywords = "Ellipsoid, Quadric, Distance, Intersection of Algebraic Manifolds",
author = "A.Y. Uteshev and M.V. Yashina",
year = "2015",
doi = "10.1016/j.jsc.2014.09.021",
language = "English",
volume = "68",
pages = "287--315",
journal = "Journal of Symbolic Computation",
issn = "0747-7171",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Metric Problems for Quadrics in Multidimensional Space

AU - Uteshev, A.Y.

AU - Yashina, M.V.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Ellipsoid

KW - Quadric

KW - Distance

KW - Intersection of Algebraic Manifolds

U2 - 10.1016/j.jsc.2014.09.021

DO - 10.1016/j.jsc.2014.09.021

M3 - Article

VL - 68

SP - 287

EP - 315

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

IS - 1

ER -

ID: 3930499