http://i48.tinypic.com/2yzd213.jpg
how they got g1 g2 g3
?
http://i48.tinypic.com/2yzd213.jpg
how they got g1 g2 g3
?
They are just different rearrangemants of $\displaystyle x^3-x-5=0$ into the form $\displaystyle x=g(x)$, presumably to show that formula iteration converges for some but not others.
$\displaystyle g_1(x)$ comes from the rearrangement $\displaystyle x=x^3-5$
$\displaystyle g_2(x)$ comes from the rearrangement $\displaystyle x^3=x-5$, so $\displaystyle x= \sqrt[3]{x-5}$
$\displaystyle g_3(x)$ comes from the rearrangement $\displaystyle x(x^2-1)-5=0$ so $\displaystyle x=\frac{5}{x^2-1}$
CB