Iteration
A repeated process where each step uses the previous result to approximate the solution of an equation.
Definition
Given an iterative formula x_(n+1) = f(x_n) and a starting value x_0, generate x_1, x_2, ... until two consecutive terms agree to the required precision. Used when an equation has no nice algebraic solution.
Example
x_(n+1) = ³√(4x_n + 2), x_0 = 2. Generates 2.154, 2.199, 2.212, 2.215, 2.216, 2.216 — root is 2.216 to 3 d.p.
Used in these topics
Practise GCSE Maths topics with instant examiner-style marking — every term in context.
Start free →