Over-constrained Weierstrass iteration and the nearest consistent system
type: Dataset
description: We propose a generalization of the Weierstrass iteration for over-constrained 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.
landing page: https://hal.science/hal-00934848
keyword: approximate-gcd
keyword: infoeu-reposemanticspreprint
keyword: infoinfo-sccomputer-science-cssymbolic-computation-cssc
keyword: iterative-method
keyword: mathmath-ocmathematics-mathoptimization-and-control-mathoc
keyword: over-constrained-algebraic-systems
keyword: preprints-working-papers-
keyword: weierstrass-method
issued: 2026-05-07T07:25:27.809020
modified: 2026-05-07T07:25:27.809025
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Over-constrained Weierstrass iteration and the nearest consistent system
type: Distribution
format: HTML
access URL: https://hal.science/hal-00934848
issued: 2026-05-07T07:25:27.810592
modified: 2026-05-07T07:25:27.798871