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A note on the finite variance of the averaging function for polynomial system solving

Abstract: In the forthcoming paper of Beltrán and Pardo, the average complexity of linear homotopy methods to solve polynomial equations with random initial input (in a sense to be described below) was proven to be finite, and even polynomial in the size of the input. In this paper, we prove that some other higher moments are also finite. In particular, we show that the variance is polynomial in the size of the input.

 Autoría: Beltrán C., Shub M.,

 Fuente: Foundations of Computational Mathematics, 2010, 10(1), 115-125

 Editorial: Springer New York LLC

 Fecha de publicación: 01/02/2010

 Nº de páginas: 11

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s10208-009-9054-4

 ISSN: 1615-3375,1615-3383

 Proyecto español: MTM2007-62799

 Url de la publicación: https://doi.org/10.1007/s10208-009-9054-4