Let us try to find $5$

$1/3$ by the fixed$-$point method. Use the fact that the result must

be the positive solution of f$($x$)=$ x

$35=0$ to solve the following:

$($a$)$ Introduce two different fixed$-$point forms which are convergent for x in $[1,2].$

$($b$)$ Perform five iterations for each of the iterations with p$0=1\mathrm{.}5,$ and measure

$|$p $$ p$5|.$

$($c$)$ Rank the associated iterations based on their apparent speed of convergence with

p$0=1\mathrm{.}5.$ Discuss why one is better than the other.