关于一类代数方程正实根的算法

ON ALGORITHM OF REAL POSITIVE ROOT OF CERTAIN ALGEBRAIC EQUATIONS

本文构造了一个求首项系数为1,而其余系数均为相等负实数的多项式方程的最大正实根μ的迭代公式.由此公式推出了μ的一个上界,该上界优于华罗庚的一个结论.本文还纠正了《欧几里得和巴拿赫空间内方程的解法》一书中的一个数值错误.

In this paper,an iteration formula used for computing the positive root of polynomial equations has been construct-ed.An upper bound of the root has been derived from.This upper bound is better than that deduced from Hua Luogen.Anumerical mistake has also been corrected in a well-known book,Solution of Equations in Euclidean and Banach Spaceswritten by A.M.Ostrowski.