On the geometry of polar varieties
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are necessary to prove the correctness and complexity estimates of these...
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Springer Verlag
2010
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| LEADER | 12071caa a22010577a 4500 | ||
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| 003 | AR-BaUEN | ||
| 005 | 20230518203801.0 | ||
| 008 | 190411s2010 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-74849106842 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a AAECE | ||
| 100 | 1 | |a Bank, B. | |
| 245 | 1 | 3 | |a On the geometry of polar varieties |
| 260 | |b Springer Verlag |c 2010 | ||
| 270 | 1 | 0 | |m Bank, B.; Humboldt-Universität zu Berlin, Institut für Mathematik, Berlin 10099, Germany; email: bank@mathematik.hu-berlin.de |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Bank, B., Giusti, M., Heintz, J., Mbakop, G.M., Polar varieties, real equation solving and data structures: The hypersurface case (1997) J. Complex. 13, pp. 5-27. , Best Paper Award J. Complexity | ||
| 504 | |a Bank, B., Giusti, M., Heintz, J., Mbakop, G.M., Polar varieties and efficient real elimination (2001) Math. Z., 238, pp. 115-144. , 10.1007/PL00004896 1860738 1073.14554 | ||
| 504 | |a Bank, B., Giusti, M., Heintz, J., Pardo, L.M., Generalized polar varieties and an efficient real elimination procedure (2004) Kybernetika, 40, pp. 519-550. , 2120995 | ||
| 504 | |a Bank, B., Giusti, M., Heintz, J., Pardo, L.M., Generalized polar varieties: Geometry and algorithms (2005) Journal of Complexity, 21 (4), pp. 377-412. , DOI 10.1016/j.jco.2004.10.001, PII S0885064X0500004X, Festschrift for the 70th Birthday of Arnold Schonhage | ||
| 504 | |a Bank, B., Giusti, M., Heintz, J., Pardo, L.M., Variétés Bipolaires et Résolution d'Une Équation Polynomiale Réelle. Preprint 09-06, , http://www.mathematik.hu-berlin.de/publ/pre/2009/p-list-09.html(2009), Humboldt-Universität zu Berlin, Institut für Mathematik | ||
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| 520 | 3 | |a We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are necessary to prove the correctness and complexity estimates of these algorithms. Our results form also the geometrical main ingredients for the computational treatment of singular hypersurfaces. In particular, we show the non-emptiness of suitable generic dual polar varieties of (possibly singular) real varieties, show that generic polar varieties may become singular at smooth points of the original variety and exhibit a sufficient criterion when this is not the case. Further, we introduce the new concept of meagerly generic polar varieties and give a degree estimate for them in terms of the degrees of generic polar varieties. The statements are illustrated by examples and a computer experiment. © 2009 Springer-Verlag. |l eng | |
| 593 | |a Humboldt-Universität zu Berlin, Institut für Mathematik, Berlin 10099, Germany | ||
| 593 | |a CNRS, École Polytechnique, Laboratoire LIX, Palaiseau Cedex 91228, France | ||
| 593 | |a Departamento de Computación, Universidad de Buenos Aires and CONICET, Ciudad Univ., Pab.I, 1428 Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina | ||
| 593 | |a Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Santander 39071, Spain | ||
| 593 | |a UPMC, Univ Paris 06, INRIA, Case 169, 4, Place Jussieu, Paris 75252, France | ||
| 593 | |a Computer Science Department, Middlesex College, University of Western Ontario, London, ON, Canada | ||
| 690 | 1 | 0 | |a REAL POLYNOMIAL EQUATION SOLVING, SINGULARITIES, CLASSIC POLAR VARIETIES, DUAL POLAR VARIETIES, GENERIC POLAR VARIETIES, MEAGERLY GENERIC POLAR VARIETIES |
| 690 | 1 | 0 | |a COMPUTATIONAL COMPLEXITY |
| 690 | 1 | 0 | |a POLYNOMIALS |
| 690 | 1 | 0 | |a ALGEBRAIC VARIETIES |
| 690 | 1 | 0 | |a COMPLEXITY BOUNDS |
| 690 | 1 | 0 | |a COMPLEXITY ESTIMATES |
| 690 | 1 | 0 | |a COMPUTER EXPERIMENT |
| 690 | 1 | 0 | |a HYPER-SURFACES |
| 690 | 1 | 0 | |a REAL POLYNOMIAL EQUATION SOLVING |
| 690 | 1 | 0 | |a SUFFICIENT CRITERION |
| 690 | 1 | 0 | |a GEOMETRY |
| 700 | 1 | |a Giusti, M. | |
| 700 | 1 | |a Heintz, J. | |
| 700 | 1 | |a Safey El Din, M. | |
| 700 | 1 | |a Schost, E. | |
| 773 | 0 | |d Springer Verlag, 2010 |g v. 21 |h pp. 33-83 |k n. 1 |p Appl Algebra Eng Commun Comput |x 09381279 |t Applicable Algebra in Engineering, Communications and Computing | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s00200-009-0117-1 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_09381279_v21_n1_p33_Bank |y Handle |
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