不用求导含参数的三阶收敛迭代方法

Third-order Convergent Iterative Method with Parameter without Derivation

基于弦截法和Steffensen迭代法,本文提出了求解非线性方程f(x)=0的两种带有参数的迭代算法,这两种算法不带有导数,且经过收敛性分析证明至少是三阶收敛的,最后用数值试验验证了本文两种迭代算法的有效性和优越性.

According to the secant method and Steffensen iterative method, this paper puts forward two iterative methods with parameters for solving the approximate solution of nonlinear equations f（x） = 0 . The two algorithms are without derivative, and we know that the two methods are at least convergent to order three through the convergence analysis and proof. Their effectiveness is validated with numerical test.