Iterative Methods of Higher Order for Nonlinear Equations

A Three-Step Iterative Method for Solving Absolute Value Equations

“…For solving the system of nonlinear equations g(x) � 0, where g: D ⊂ R ⟶ R, many methods are given in [13][14][15], these methods also give us a lot of good ideas. Taking some of the advantages of the above approach, considering the particularity of the system of absolute value equations, this paper designed the following three-step iterative algorithm for AVEs (1).…”

“…Salkuyeh [8] presented the Picard-HSS iteration method for solving the system of absolute value equations, and there are also two CSCSbased iteration methods [9] and other iterative algorithms [10][11][12]. In addition, some iterative algorithms for solving the system of nonlinear equations are also interesting, for example, many three-step higher-order iterative algorithms are designed to solve the system nonlinear equations [13], Cordero et al proposed two iterative algorithms with fourth-order and fifth-order convergences to solve the system nonlinear equations in [14].…”

A new two-step iterative method for solving absolute value equations

“…Some iterative methods with higher order convergence and high precision for solving nonlinear equations g(x) = 0, where g : D ⊂ R → R, are in [18], which give us some inspiration and motivate us to extend those methods to the n-dimensional problem, especially the high-dimensional absolute value equations. Combining with the above-mentioned methods, we designed the following effective methods.…”

The Local Convergence of a Three-Step Sixth-Order Iterative Approach with the Basin of Attraction

“…This method is known for its quadratic convergence. To enhance the efficiency and order of convergence [2], many scholars have introduced iterative techniques with a higher order of convergence and higher efficiency. Several important methods with third-order convergence are given in [3][4][5]; some of the important methods with fourth-order convergence are given in [6,7]; an important method with fifth-order convergence is given in [8,9].…”