Iteration is a numerical method used to find an approximation to a root (solution) of an equation y=f(x) where f(x)=0.

The method discussed here is often known as fixed point iteration.

Iteration – Finding an approximate solution to f(x)=0

Iteration - Solving equations (1 of 2) | ExamSolutions - youtube Video

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How it works

Iteration - See how it works (2 of 2) | ExamSolutions - youtube Video

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For further demonstration and examples see this Desmos presentation