Perturbation results on the zero-locus of a polynomial. (May 2017)

• Record Type: Journal Article
• Authors: Torrente, Maria-Laura; Beltrametti, Mauro C.; Sommese, Andrew J.
• Is Part Of: Journal of symbolic computation. Volume 80:Part 2(2017)
• Page Start: 307
• Page End: 328
• Publication Date: 2017-05
• Subjects: primary 65H04 26C10 -- secondary 15A60; Bombieri's norm -- Walsh's Contraction Principle -- Location of zeros of multivariate polynomials -- Perturbations of real polynomials; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.04.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let f and g be complex multivariate polynomials of the same degree. Extending Beauzamy's results which hold in the univariate case, we bound the Euclidean distance of points belonging to the zero-loci of f and g in terms of the Bombieri norm of the difference g − f . We also discuss real perturbations of real polynomials.