Computing Assignment $$ Floating Point Arithmetic

Required submission: $1$ page PDF document and Matlab scripts uploaded to Canvas.

Let x $>=0$ be an arbitrary number and n a nonnegative integer. In exact arithmetic, the following computation leaves x unchanged:$1234567$

for i$=1$:n

x$=$sqrt$($x$)$;

end

for i$=1$:n

x$=$x$2$;

end$$However$,$ in finite$-$precision arithmetic the results may be dramatically different for large n$.$ The purpose of this assignment is to investigate the output of this computation in Matlab for various values of n and for x in the range $0<=$ x $<=5.$

Your conclusions should be explained in a one$-$page report. Your report must include the following:

$($a$)$ Representative plots of the output as a function of x$,$ with each plot corresponding to a

different value of n$.$

$($b$)$ A discussion of the smallest value of n after which the result of the finite$-$precision computation

begins to differ from exact arithmetic computation.

$($c$)$ A discussion of the limiting behaviour for large n$.$

$($d$)$ A brief explanation as to why computing in floating point arithmetic leads to the results you have found.

Partial code for this assignment can be found in the file FloatPt.m on Canvas. I suggest using this as your starting point. If you have questions about Matlab or other aspects of the assignment or course, then I strongly encourage you to attend the tutorials and drop$-$in workshops.