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

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 dim...

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Bibliographic Details
Published in:Mathematics of computation 2007-07, Vol.76 (259), p.1393-1424
Main Authors: Beltrán, C., Pardo, L. M.
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Algorithms
Exact sciences and technology
Global analysis, analysis on manifolds
Integers
Mathematical theorems
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Newtons method
Numerical analysis
Numerical analysis. Scientific computation
Polynomials
Probability distributions
Radii of convergence
Real numbers
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-07-01963-1