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Item type:Publication, Access status: without files , Improvements of Lagrange's bound for polynomial roots(2017-09-01); ; 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.Publicationtype: Journal Article143