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 (xn+1 = g(x_n) ).
[b]uConverging iterations[/u]/b
Some iterations will bconverge/b to a root. If this happens from the same direction, the representation on a graph is known as a bstaircase diagram/b.
mtaimg/images/topics/9/9-100-1.png/mtaimg
If this happens by alternating above and below the root, the representation on a graph is known as a bcobweb diagram/b.
mtaimg/images/topics/9/9-100-2.png/mtaimg
[b]uDiverging iterations[/u]/b
Not iterations converge to a root. Sometimes, iterations can bdiverge/b away from the root. In this case, it will be impossible to obtain a solution for the root.
mtaimg/images/topics/9/9-100-3.png/mtaimg
[b]uIterative methods[/u]/b
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 (xn+1 = g(x_n) ).