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.

• Content Type Journal Article
• DOI 10.1007/s10208-009-9054-4
• Authors
  
  
  • Carlos Beltrán, Universidad de Cantabria Departamento de Matemáticas, Estadística y Computación Santander Spain
  • Michael Shub, University of Toronto Department of Mathematics Toronto Ontario Canada M5S 2E4
  
  

• Journal Foundations of Computational Mathematics
• Online ISSN 1615-3383
• Print ISSN 1615-3375

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Original source : http://www.springerlink.com/content/85716269n07w52...