How to Choose a Root Finding Algorithm?

Choosing a root finding algorithm depends on several factors:

Function Properties: Consider whether the function is continuous, differentiable, and how well-behaved it is.
Initial Knowledge: Determine if you have an initial interval containing the root or just a rough estimate.
Accuracy Requirements: Assess how accurate the root approximation needs to be.
Computational Resources: Consider the computational complexity and resources available.
Robustness: Evaluate how robust the algorithm is against different function behaviors and initial guesses.
Speed: Balance between convergence speed and computational efficiency.
Dimensionality: For higher-dimensional problems, choose algorithms that extend well to multiple dimensions.

Root Finding Algorithm

Root-finding algorithms are tools used in mathematics and computer science to locate the solutions, or “roots,” of equations. These algorithms help us find solutions to equations where the function equals zero. For example, if we have an equation like f(x) = 0, a root-finding algorithm will help us determine the value of x that makes this equation true.

In this article, we will explore different types of root finding algorithms, such as the bisection method, Regula-Falsi method, Newton-Raphson method, and secant method. We’ll explain how each algorithm works, and how to choose the appropriate algorithm according to the use case.

Table of Content

What is a Root Finding Algorithm?
Types of Root Finding Algorithms
Bracketing Methods

Bisection Method
False Position (Regula Falsi) Method

Open Methods

Newton-Raphson Method
Secant Method