Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
436147 | Theoretical Computer Science | 2015 | 19 Pages |
Abstract
We propose a generalization of the Weierstrass iteration for overdetermined systems of equations and we prove that the proposed method is the Gauss–Newton iteration to find the nearest system which has at least k common roots and which is obtained via a perturbation of prescribed structure. In the univariate case we show the connection of our method to the optimization problem formulated by Karmarkar and Lakshman for the nearest GCD. In the multivariate case we generalize the expressions of Karmarkar and Lakshman, and give explicitly several iteration functions to compute the optimum. The arithmetic complexity of the iterations is detailed.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Olivier Ruatta, Mark Sciabica, Agnes Szanto,