## 9.2 Iterative methods

Iterative methods can be used to solve equations which are otherwise difficult or impossible to solve.

To solve an equation of the form $$f(x) = 0$$ using an iterative method, rearrange $$f(x) = 0$$ into the form $$x = g(x)$$ and use the iterative formula $$x_{n+1} = g(x_n)$$.

Converging iterations

Some iterations will converge to a root. If this happens from the same direction, the representation on a graph is known as a staircase diagram.

If this happens by alternating above and below the root, the representation on a graph is known as a cobweb diagram.

Diverging iterations

Not iterations converge to a root. Sometimes, iterations can diverge away from the root. In this case, it will be impossible to obtain a solution for the root.

Important
Iterative methods

To solve an equation of the form $$f(x) = 0$$ using an iterative method, rearrange $$f(x) = 0$$ into the form $$x = g(x)$$ and use the iterative formula $$x_{n+1} = g(x_n)$$.
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