Krandick's proof of Lagrange's real root bound claim. (September 2015)

• Record Type: Journal Article
• Authors: Collins, George E.
• Is Part Of: Journal of symbolic computation. Volume 70(2015)
• Page Start: 106
• Page End: 111
• Publication Date: 2015-09
• Subjects: Root bounds -- Lagrange bound -- Hong bound -- Radicals -- Real roots; 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.2014.09.038
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In 1879 Lagrange asserted without a proof that a certain sum of two radicals would always be an upper bound on the positive roots of any polynomial having a positive leading coefficient and at least two negative coefficients. The claim was nearly forgotten and never proved. This paper provides a nontrivial proof by Krandick and his application of the resulting theorem to an improvement of the very effective Hong root bound.