An iteration/root finding algorithm is a mathematical procedure used to approximate the solutions of a given equation or system of equations. It involves repeatedly evaluating a function at different input values until a desired level of accuracy is achieved.
An iteration algorithm starts with an initial guess for the solution and then uses a predetermined formula to update that guess with each iteration. The process continues until the updated guess is close enough to the actual solution, as determined by a specified tolerance level.
The terms "iteration algorithm" and "root finding algorithm" are often used interchangeably, but there is a subtle difference between the two. While an iteration algorithm uses a specific formula to update the initial guess, a root finding algorithm can use a variety of techniques, such as bisection, Newton's method, or the secant method, to find the solution.
Iteration/root finding algorithms can be used to solve a wide range of equations, including polynomial equations, transcendental equations, and systems of equations. They can also be applied to optimization problems, where the goal is to find the maximum or minimum value of a function.
Iteration/root finding algorithms are very versatile and can be applied to a variety of problems. They also have the advantage of being relatively easy to implement and can often provide a solution even when a closed-form solution is not available. Additionally, these algorithms can handle complex equations and systems that may not have a straightforward solution.