【摘要】 通过对强函数的分析将Smale在1986年数学大会上的报告的关于Newton.迭代点估计的工作推广到简化Newton法,证明了当a（z.f）≤1/13时.对于所有实的或复的Banach空间E到同类空间F的解析映射f和Z∈E.Z是f的一个逼近零点.而当a（z.f）≤(9-（61）^1/2)/6时.z是f的一个第二类逼近零点.更多还原

【Abstract】 Smale’s work on point estimates for Newton’s method, which was reported on international congress of Mathematicians, was exlended to simplified Newton’s method through analysing merit function. It was proved that for any analytic map / from one Ba-nach space E (real or complex) to space F of the same type and any z∈E ,if α(z,f)≤1/13, then z is a approximate Zero point, and if α(z,f)≤9-61/16,then z is a second classapproximate Zero point of f.更多还原