Distance bounds of ϵ-points on hypersurfaces
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 li...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/49600 |
| Acceso en línea: | http://hdl.handle.net/10017/49600 https://dx.doi.org/10.1016/j.tcs.2006.05.020 |
| Access Level: | acceso abierto |
| Palabra clave: | ϵ-points Distance bounds Hypersurfaces Approximate algorithms Matemáticas Mathematics |
| Sumario: | 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. |
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