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

Beltrán, C.; Pardo, L.

doi:10.1090/S0025-5718-07-01963-1

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
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by C. Beltrán and L. M. Pardo;

Math. Comp. 76 (2007), 1393-1424

DOI: https://doi.org/10.1090/S0025-5718-07-01963-1

Published electronically: February 5, 2007

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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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