Abstract:
In previous work we designed an efficient procedure that finds an algebraic sample point for each connected component of a smooth real complete intersection variety. This procedure exploits geometric properties of generic polar varieties and its complexity is intrinsic with respect to the problem. In the present paper we introduce a natural construction that allows to tackle the case of a non-smooth real hypersurface by means of a reduction to a smooth complete intersection. © 2009 Elsevier B.V. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | On the intrinsic complexity of point finding in real singular hypersurfaces |
Autor: | Bank, B.; Giusti, M.; Heintz, J.; Pardo, L.M. |
Filiación: | Humboldt-Universität zu Berlin, Institut für Mathematik, D-10099 Berlin, Germany CNRS, École Polytechnique, Laboratoire LIX, F-91228 Palaiseau Cedex, France Departamento de Computación, Universidad de Buenos Aires, CONICET, Pab. I, 1428 Ciudad Autonoma de Buenos Aires, Argentina Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain
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Palabras clave: | Computational complexity; Real polynomial equation solving; Singular hypersurface; Computational complexity; Computer applications; Data processing; Complete intersection; Connected component; Geometric properties; Hyper-surfaces; Hypersurface; Real polynomial equation solving; Sample point; Polynomials |
Año: | 2009
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Volumen: | 109
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Número: | 19
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Página de inicio: | 1141
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Página de fin: | 1144
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DOI: |
http://dx.doi.org/10.1016/j.ipl.2009.07.014 |
Título revista: | Information Processing Letters
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Título revista abreviado: | Inf. Process. Lett.
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ISSN: | 00200190
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CODEN: | IFPLA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00200190_v109_n19_p1141_Bank |
Referencias:
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- Bank, B., Giusti, M., Heintz, J., Mbakop, G.M., Polar varieties and efficient real elimination (2001) Math. Z., 238, pp. 115-144
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- Safey El Din, M., (2005) Finding sampling points on real hypersurfaces is easier in singular situations, , http://www-spiral.lip6.fr/~safey/publi.html, prepublication
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Citas:
---------- APA ----------
Bank, B., Giusti, M., Heintz, J. & Pardo, L.M.
(2009)
. On the intrinsic complexity of point finding in real singular hypersurfaces. Information Processing Letters, 109(19), 1141-1144.
http://dx.doi.org/10.1016/j.ipl.2009.07.014---------- CHICAGO ----------
Bank, B., Giusti, M., Heintz, J., Pardo, L.M.
"On the intrinsic complexity of point finding in real singular hypersurfaces"
. Information Processing Letters 109, no. 19
(2009) : 1141-1144.
http://dx.doi.org/10.1016/j.ipl.2009.07.014---------- MLA ----------
Bank, B., Giusti, M., Heintz, J., Pardo, L.M.
"On the intrinsic complexity of point finding in real singular hypersurfaces"
. Information Processing Letters, vol. 109, no. 19, 2009, pp. 1141-1144.
http://dx.doi.org/10.1016/j.ipl.2009.07.014---------- VANCOUVER ----------
Bank, B., Giusti, M., Heintz, J., Pardo, L.M. On the intrinsic complexity of point finding in real singular hypersurfaces. Inf. Process. Lett. 2009;109(19):1141-1144.
http://dx.doi.org/10.1016/j.ipl.2009.07.014