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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
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
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
Volumen:109
Número:19
Página de inicio:1141
Página de fin:1144
DOI: http://dx.doi.org/10.1016/j.ipl.2009.07.014
Título revista:Information Processing Letters
Título revista abreviado:Inf. Process. Lett.
ISSN:00200190
CODEN:IFPLA
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
  • Bank, B., Giusti, M., Heintz, J., Pardo, L.M., Generalized polar varieties and an efficient real elimination procedure (2004) Kybernetika (Prague), 40, pp. 519-550
  • Bank, B., Giusti, M., Heintz, J., Pardo, L.M., Generalized polar varieties: Geometry and algorithms (2005) J. Complexity, 21, pp. 377-412
  • Bank, B., Giusti, M., Heintz, J., Safey El Din, M., Schost, E., On the geometry of polar varieties, AAECC (2009), , http://www.mathematik.hu-berlin.de/publ/pre/2009/P-09-10.pdf, submitted for publication
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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