Writeafunctionwithheader$[$X$]=$ myFixedPoint$($f$,$g$,$tol,maxIter$),$wherefand

gare function handles and tol and maxIterarestrictly positive scalars. The input argument,

maxIter, is also an integer. The output argument, X$,$ should be a scalar satisfying $|$ f $($X$)$

g$($X$)|<$ tol; that is$,$ X is a point that $($almost$)$ satisfies f$($X$)=$ g$($X$).$ To find X$,$ you should

use the Bisection method with error metric, $|$F$($m$)|<$ tol. The function myFixedPoint

should $$give up$$ after maxIter number of iterations and return X $=[]$if this occurs.

Test Cases:

$>>$f $=$ @$($x$)$ x$.^2-2$;

$>>[$R$,$E$]=$ myBisection$($f$,0,2,1$e$-1)$

R $=$

$1\mathrm{.}00001\mathrm{.}50001\mathrm{.}25001\mathrm{.}37501\mathrm{.}4375$

E $=$

$1\mathrm{.}00000\mathrm{.}25000\mathrm{.}43750\mathrm{.}10940\mathrm{.}0664$

$>>$f $=$ @$($x$)$sin$($x$)-$cos$($x$)$;

$>>[$R$,$E$]=$ myBisection$($f$,0,2,1$e$-2)$

R $=$

$1\mathrm{.}00000\mathrm{.}50000\mathrm{.}75000\mathrm{.}87500\mathrm{.}8125$

E $=$

$0\mathrm{.}30120\mathrm{.}39820\mathrm{.}05010\mathrm{.}12650\mathrm{.}0383$