两类新的求解非线性方程的四阶方法(英文)

Two new families of fourth order methods for solving non-linear equations

应用待定系数法和权函数法给出了在实数域R上求解非线性方程单根的2类新的四阶方法.考虑了计算效率,本方法每步需要计算1个函数值,2个导数值,效率指数为1.587.通过新方法与牛顿法及其他已知方法的比较,结果表明新方法具有一定的优越性.

Two new families of fourth order methods are developed for finding the simple roots of nonlinear equations in R by using the methods of undetermined coefficients and weight functions. In terms of computational cost, they require evaluations of only one function and two first derivatives per iteration. This implies that the efficiency index of the new methods is 1. 587. The new methods are comparable with Newton method and other existing methods, as shown in the illustration examples.