33 citations · 81 across the 24 of their papers we have counts for
3 papers · 1 filter
Certifying solutions to overdetermined and singular polynomial systems over Q
Tulay Ayyildiz Akoglu, Jonathan D. Hauenstein, Agnes Szanto
This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies…
Global Newton Iteration over Archimedean and non-Archimedean Fields
Jonathan D. Hauenstein, Victor Pan, Agnes Szanto
In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare t…
Over-constrained Weierstrass iteration and the nearest consistent system
Olivier Ruatta, Mark Sciabica, Agnes Szanto
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 n…