Open Methods: Introduction

Open methods do not rely on having the root squeezed between two values, but rather rely on an initial guess and then apply an iterative process to get better estimates for the root. Open methods are usually faster in convergence if they converge, but they don’t always converge. For multi-dimensions, i.e., for solving multiple nonlinear equations, open methods are easier to implement than bracketing methods which cannot be easily extended to multi-dimensions. We are going to present three open methods: Fixed-Point Iteration Method, Newton Raphson Method, and the Secant Method.