Standard

Computation of the distance from an ellipsoid to a linear surface and a quadric in n. / Uteshev, A. Yu; Yashina, M. V.

в: Doklady Mathematics, Том 77, № 2, 01.04.2008, стр. 269-272.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Uteshev, AY & Yashina, MV 2008, 'Computation of the distance from an ellipsoid to a linear surface and a quadric in n', Doklady Mathematics, Том. 77, № 2, стр. 269-272. https://doi.org/10.1134/S1064562408020270

APA

Uteshev, A. Y., & Yashina, M. V. (2008). Computation of the distance from an ellipsoid to a linear surface and a quadric in n. Doklady Mathematics, 77(2), 269-272. https://doi.org/10.1134/S1064562408020270

Vancouver

Uteshev AY, Yashina MV. Computation of the distance from an ellipsoid to a linear surface and a quadric in n. Doklady Mathematics. 2008 Апр. 1;77(2):269-272. https://doi.org/10.1134/S1064562408020270

Author

Uteshev, A. Yu ; Yashina, M. V. / Computation of the distance from an ellipsoid to a linear surface and a quadric in n. в: Doklady Mathematics. 2008 ; Том 77, № 2. стр. 269-272.

BibTeX

@article{6efd4c2a38cc41cd931791df265d7e58,
title = "Computation of the distance from an ellipsoid to a linear surface and a quadric in n",
abstract = "A study was conducted to compute the distance from an ellipsoid to a linear surface and a quadric in Rn1 and to investigate the closeness of objects in an n-dimensional parametric space in computational geometry and pattern recognition problem. The study found that the optimization problem of these is reduced by traditional application of LaGrange multipliers to a problem of solving a system of algebraic equations. The study stated that eliminate all variables from the system and construct an algebraic equation to evaluate the coordinates of the nearest points. The coordinates of the nearest points on the given surface can be expressed as a rational function in terms of this value. The study found that the procedure used is implemented by constructing a Gr{\"o}bner basis and the methods of classical elimination theory.",
author = "Uteshev, {A. Yu} and Yashina, {M. V.}",
year = "2008",
month = apr,
day = "1",
doi = "10.1134/S1064562408020270",
language = "English",
volume = "77",
pages = "269--272",
journal = "Doklady Mathematics",
issn = "1064-5624",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "2",

}

RIS

TY - JOUR

T1 - Computation of the distance from an ellipsoid to a linear surface and a quadric in n

AU - Uteshev, A. Yu

AU - Yashina, M. V.

PY - 2008/4/1

Y1 - 2008/4/1

N2 - A study was conducted to compute the distance from an ellipsoid to a linear surface and a quadric in Rn1 and to investigate the closeness of objects in an n-dimensional parametric space in computational geometry and pattern recognition problem. The study found that the optimization problem of these is reduced by traditional application of LaGrange multipliers to a problem of solving a system of algebraic equations. The study stated that eliminate all variables from the system and construct an algebraic equation to evaluate the coordinates of the nearest points. The coordinates of the nearest points on the given surface can be expressed as a rational function in terms of this value. The study found that the procedure used is implemented by constructing a Gröbner basis and the methods of classical elimination theory.

AB - A study was conducted to compute the distance from an ellipsoid to a linear surface and a quadric in Rn1 and to investigate the closeness of objects in an n-dimensional parametric space in computational geometry and pattern recognition problem. The study found that the optimization problem of these is reduced by traditional application of LaGrange multipliers to a problem of solving a system of algebraic equations. The study stated that eliminate all variables from the system and construct an algebraic equation to evaluate the coordinates of the nearest points. The coordinates of the nearest points on the given surface can be expressed as a rational function in terms of this value. The study found that the procedure used is implemented by constructing a Gröbner basis and the methods of classical elimination theory.

UR - http://www.scopus.com/inward/record.url?scp=43049092642&partnerID=8YFLogxK

U2 - 10.1134/S1064562408020270

DO - 10.1134/S1064562408020270

M3 - Article

AN - SCOPUS:43049092642

VL - 77

SP - 269

EP - 272

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -

ID: 42730324