Improvements of Lagrange's bound for polynomial roots
Publikationstyp
Journal Article
Date Issued
2017-09-01
Sprache
English
Institut
TORE-URI
Volume
82
Start Page
19
End Page
25
Citation
Journal of Symbolic Computation (82): 19-25 (2017-09-01)
Publisher DOI
Scopus ID
An upper bound for the roots of Xd+a1Xd−1+⋯+ad−1X+ad is given by the sum of the largest two of the terms |ai|1/i. This bound by Lagrange has gained attention from different sides recently, while a succinct proof seems to be missing. We present a short, original proof of Lagrange's bound. Our approach leads to some definite improvements. To benefit computationally from these improvements, we construct a modified Lagrange bound which at the same asymptotic computational complexity is at most 11 per cent from optimal for degrees d≥16.
Subjects
Complex roots
Computational effort
Overestimation factor