TY - GEN

T1 - Approximation of the Distance from a Point to an Algebraic Manifold

AU - Uteshev, Alexei

AU - Goncharova, Marina

N1 - Uteshev, A. and Goncharova, M. (2019). Approximation of the Distance from a Point to an Algebraic Manifold.In Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-758-351-3, pages 715-720. DOI: 10.5220/0007483007150720

PY - 2019

Y1 - 2019

N2 - The problem of geometric distance d evaluation from a point X0 to an algebraic curve in R2 or manifold G(X) = 0 in R3 is treated in the form of comparison of exact value with two its successive approximations d(1) and d(2). The geometric distance is evaluated from the univariate distance equation possessing the zero set coinciding with that of critical values of the function d2(X0), while d(1)(X0) and d(2)(X0) are obtained via expansion of d2(X0) into the power series of the algebraic distance G(X0). We estimate the quality of approximation comparing the relative positions of the level sets of d(X), d(1)(X) and d(2)(X).

AB - The problem of geometric distance d evaluation from a point X0 to an algebraic curve in R2 or manifold G(X) = 0 in R3 is treated in the form of comparison of exact value with two its successive approximations d(1) and d(2). The geometric distance is evaluated from the univariate distance equation possessing the zero set coinciding with that of critical values of the function d2(X0), while d(1)(X0) and d(2)(X0) are obtained via expansion of d2(X0) into the power series of the algebraic distance G(X0). We estimate the quality of approximation comparing the relative positions of the level sets of d(X), d(1)(X) and d(2)(X).

KW - Algebraic Manifold

KW - Level Set

KW - Discriminant

KW - Distance Approximation

KW - Algebraic Manifold

KW - Discriminant

KW - Distance Approximation

KW - Level Set

UR - http://www.scopus.com/inward/record.url?scp=85064632653&partnerID=8YFLogxK

UR - http://www.scitepress.org/DigitalLibrary/Link.aspx?doi=10.5220/0007271903420351

UR - http://www.mendeley.com/research/physical-activity-recognition-utilising-smartphone-sensor-signals

M3 - Conference contribution

VL - 1

SP - 715

EP - 720

BT - Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods

A2 - Fred, Ana

A2 - De Marsico, Maria

A2 - di Baja, Gabriella Sanniti

PB - SciTePress

T2 - 8th International Conference on Pattern Recognition Applications and Methods

Y2 - 19 February 2019 through 21 February 2019

ER -