【摘要】 1973年,R.F.King提出了一族4阶迭代函数φ_β(x)=u(x)-f(u(x))/f′(x){f(x)+βf(u(x))/f(x)+(β-2)f(u(x))} 其中,u(x)=x-f(x)/f′(x),β是实参数。本文提供了一种选择参数β的方法,使其收敛阶可达到5,并证明了当β∈[0,2]时King迭代法的一个收敛定理,同时还给出了一些数值例子。更多还原

【Abstract】 In 1973, R. F. King suggested a family of iterative functions with the form φβ(x)=μ(x)-f(μ(x))/f’(x){f(x)+βf(μ(x))/f(x)+(β-2)f(μ(x))where μ(x)=x-f(x)/f’(x) β is a real parameter. The convergence order of theiterations is 4. This paper presents a method for choosing the parameter β so that theconvergence order can reach 5. A convergence theorem for the King’s iterations withβ∈[0,2] is proved. Some numerical examples are also given here.更多还原