Zero-dimensional families of polynomial systems
Abstract
If a real world problem is modelled with a system of polynomial equations, the coefficients are in general not exact. The consequence is that small perturbations of the coefficients may lead to big changes of the solutions. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first part we show how to construct semi-algebraic sets in the parameter space over which the family of all ideals shares the number of isolated real zeros. In the second part we show how to modify the equations and get new ones which generate the same ideal, but whose real zeros are more stablewith respect to perturbations of the coefficients.
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
