Paper Info
Title
Numerically validating the completeness of the real solution set of a system of polynomial equations.
Abstract
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares programming to test whether a given set is complete with respect to the real solution set. Specifically, we test whether the Zariski closure of that given set is indeed equal to the solution set of the real radical of the ideal generated by the given polynomials. Examples with finitely and infinitely many real solutions are provided, along with an example having polynomial inequalities.
Year
Venue
Field
2016
arXiv: Numerical Analysis
Set function,Polynomial,Algebra,Mathematical analysis,System of polynomial equations,Numerical algebraic geometry,Solution set,Polynomial inequalities,Completeness (statistics),Mathematics
DocType
Volume
Citations 
Journal
abs/1602.00700
3
PageRank 
References 
Authors
0.54
14
3
Name
Order
Citations
PageRank
Daniel A. Brake1173.56
Jonathan D. Hauenstein226937.65
Alan C. Liddell Jr.3182.88