Solving a nonlinear equation by a uniparametric family of iterative processes

Abstract

In this study, we introduce a family of third-order iterative methods, cited in [4], for solving a nonlinear equation f(x) = 0. First we provide a convergence analysis for a real function depending of one real parameter α ∊ . Next it is proved that we can always apply a method of this family to solve f(x) = 0.

Keywords:

• Nonlinear equations
• iterative process
• Chebyshev's method
• the Convex Acceleration of Newton's method

Mathematical Subject Classification:

• 65H05

C.R. Categories:

• G.1.3