RT info:eu-repo/semantics/article
T1 Distance bounds of ϵ-points on hypersurfaces
A1 Pérez Díaz, Sonia
A1 Sendra Pons, Juana
A1 Sendra Pons, Juan Rafael
K1 ϵ-points
K1 Distance bounds
K1 Hypersurfaces
K1 Approximate algorithms
K1 Matemáticas
K1 Mathematics
AB ϵ-points were introduced by the authors (see [S. Pérez-Díaz, J.R. Sendra, J. Sendra, Parametrization of approximate algebraic curves by lines, Theoret. Comput. Sci. 315(2–3) (2004) 627–650 (Special issue); S. Pérez-Díaz, J.R. Sendra, J. Sendra, Parametrization of approximate algebraic surfaces by lines, Comput. Aided Geom. Design 22(2) (2005) 147–181; S. Pérez-Díaz, J.R. Sendra, J. Sendra, Distance properties of ϵ-points on algebraic curves, in: Series Mathematics and Visualization, Computational Methods for Algebraic Spline Surfaces, Springer, Berlin, 2005, pp. 45–61]) as a generalization of the notion of approximate root of a univariate polynomial. The notion of ϵ-point of an algebraic hypersurface is quite intuitive. It essentially consists in a point such that when substituted in the implicit equation of the hypersurface gives values of small module. Intuition says that an ϵ-point of a hypersurface is a point close to it. In this paper, we formally analyze this assertion giving bounds of the distance of the ϵ-point to the hypersurface. For this purpose, we introduce the notions of height, depth and weight of an ϵ-point. The height and the depth control when the distance bounds are valid, while the weight is involved in the bounds.
PB Elsevier
SN 0304-3975
YR 2006
FD 2006
LK http://hdl.handle.net/10017/49600
UL http://hdl.handle.net/10017/49600
LA eng
NO Ministerio de Educación y Ciencia
DS MINDS@UW
RD 07-jun-2023