2011/02/10 by Lorenzo Robbiano, Maria-Laura Torrente, Robbiano, Lorenzo +2
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC
paper · pdf · doi:10.48550/arxiv.1102.2158
1 figure
arxiv created 2011/02/10 · openalex publication_date 2011/02/10 · arxiv updated 2011/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A complete intersection of n polynomials in n indeterminates has only a finite number of zeros. 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 all the complete intersection ideals share the same number of isolated real zeros. In the second part we show how to modify the complete intersection and get a new one which generates the same ideal but whose real zeros are more stable with respect to perturbations of the coefficients.