Iteration
Definition
An iteration is a term used in various fields, including mathematics, computer science, and project management, to denote the act of repeating a process with the aim of approaching a desired goal, target, or result. Each repetition of the process is also called an iteration, and the results of one iteration are used as the starting point for the next iteration Iteration in Mathematics.
Mathematics
In mathematics, an iteration refers to the process of repeating a mathematical procedure, each time applying it to the result of the previous application. It is a fundamental concept in numerous areas of mathematics, including numerical analysis, dynamical systems, and fractals.
Numerical Analysis
In numerical analysis, iteration is used to approximate solutions of equations. For example, the Newton-Raphson method is an iterative method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
Dynamical Systems
In the study of dynamical systems, iteration is used to describe the behavior of a system over time. In this context, the result of one iteration serves as the initial condition for the next.
Fractals
In the field of fractals, iteration is used to generate complex shapes. The most famous example is the Mandelbrot set, which is created by iterating a simple complex number equation.
Computer Science
In computer science, iteration refers to the technique of controlling program flow with loops. There are three primary types of loops: for, while, and do-while. Each of these loops represents a different way to perform iteration, but they all accomplish the same basic task: repeating a block of code multiple times Iteration in Computer Science.
For Loop
A for loop is a control flow statement for specifying iteration, which allows code to be executed repeatedly. The loop is characterized by a three-part loop control expression; consisting of an initializer, a condition, and an increment (or decrement) operator.
While Loop
A while loop is a control flow statement that allows code to be executed repeatedly based on a given Boolean condition. The while loop can be thought of as a repeating if statement.
Do-While Loop
A do-while loop is similar to a while loop, except the fact that it is guaranteed to execute at least one time, because it first checks the condition after the loop has executed.
Project Management
In project management, iteration refers to a single development cycle in a project following the Agile methodology. Each iteration is a standard, fixed length of time, and it is sequentially numbered with the start of the project.
