单变量函数方程求根的一种新型大范围收敛迭代法

A new type of globally convergent iterative method for solving functional equations of one variable

对求解函数方程f(x)=0提出了一种新型大范围收敛迭代法,该方法每次迭代仅需计算一个f值,其收敛阶与有效指数相同,约在1.618与1.839之间。通过给出的实例比较表明,该方法具有明显优势。

Concerning the solving of function equations f(x) = 0, a new type of globally convergent iterative method is given. In its every iterative step, only one function evaluation for f is required. Its convergence order and effective index are the same, the range is ρ1≈1.681 and ρ2 ≈1.839. Concrete examples indicate that this method possesses superiority.