A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations

[摘要] We present two new families of iterative methods for obtaining simpleroots of nonlinear equations. The first family is developed by fitting the modelm(x)=epx(Ax2+Bx+C)to the functionf(x)and its derivativef′(x),f″(x)at a pointxn. In order to remove the second derivative of the first methods, we construct the secondfamily of iterative methods by approximating the equationf(x)=0around the point(xn,f(xn))by the quadratic equation. Analysis of convergence shows that the newmethods have third-order or higher convergence. Numerical experiments show thatnew iterative methods are effective and comparable to those of the well-known existingmethods.

[学科分类] 应用数学