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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the probability distribution of condition numbers of complete intersection varieties and the average radius of convergence of Newton's method in the underdetermined case


Authors: C. Beltrán and L. M. Pardo
Journal: Math. Comp. 76 (2007), 1393-1424
MSC (2000): Primary 65G50, 65H10
Published electronically: February 5, 2007
MathSciNet review: 2299780
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Abstract: In these pages we show upper bound estimates on the probability distribution of the condition numbers of smooth complete intersection algebraic varieties. As a by-product, we also obtain lower bounds for the average value of the radius of Newton's basin of attraction in the case of positive dimension affine complex algebraic varieties.


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Additional Information

C. Beltrán
Affiliation: Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, E–39071 Santander, Spain
Email: beltranc@unican.es

L. M. Pardo
Affiliation: Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, E–39071 Santander, Spain
Email: luis.pardo@unican.es

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01963-1
PII: S 0025-5718(07)01963-1
Keywords: Condition number, geometric integration theory
Received by editor(s): February 6, 2006
Published electronically: February 5, 2007
Additional Notes: This research was partially supported by MTM2004-01167 and FPU program, Government of Spain
Article copyright: © Copyright 2007 American Mathematical Society