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.

__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 \(x_{n+1} = g(x_n) \).

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 \(x_{n+1} = g(x_n) \).

Some iterations will

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

Not iterations converge to a root. Sometimes, iterations can

Important

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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