The Bisection Method of Root-Finding with R

The bisection method is another approach to finding the root of a continuous function [latex]f(x)[/latex] on an interval [latex][a, b][/latex]. The method takes advantage of a corollary of the intermediate value theorem called Bolzano’s theorem which states that if the values of [latex]f(a)[/latex] and [latex]f(b)[/latex] have opposite signs, the interval...

The Secant Method Root-Finding Algorithm in R

The secant method for finding roots of nonlinear equations is a common and popular variation of the Newton-Raphson method that has been used for several millennia before the invention of Newton-Raphson (Papakonstantinou, J. as cited in Wikipedia). The secant method is an iterative method that takes two initial guesses of...

The Newton-Raphson Root-Finding Algorithm in R

The Newton-Raphson method is an approach for finding the roots of nonlinear equations and is one of the most common root-finding algorithms due to its relative simplicity and speed. The root of a function is the point at which [latex]f(x) = 0[/latex]. Many equations have more than one root. Every...