Two Modified Newton-Type Iterative Methods for Solving Nonlinear Equations

摘要

With the rapid development of information science and engineering technology, nonlinear problems become an important research in the field of numerical analysis. In this paper, iterative methods for solving nonlinear equations are researched. Two modified Newton-type algorithms for solving nonlinear equations are proposed and analyzed, whose order of convergence are six and seven respectively. Both of the methods are free from second derivatives. The efficiency index of the presented methods are 1.431 and 1.476, respectively, which are all better than that of the classical Newton's method 1.414. Some numerical experiments demonstrate the performance of the presented algorithms.