$.$ The double sum starts in the lower left corner, goes up the column $1$ values, then down to the bottom of column $2$ then up$,$ and so on$.$

In theory, the result should be more accurate as n gets large. BUT as n gets very large, the error actually increases!!

Indeed, the errors for n$=5,50,500,$ and $5000$ are listed below

Grid Size$($n x n$)$ Relative Error

n$=51\mathrm{.}28$e$-03$

n$=501\mathrm{.}31$e$-04$

n$=5005\mathrm{.}01$e$-06$

n$=50007\mathrm{.}22$e$-02($WTH$?)$

Your Job: Add up the numbers f$($x$,$y$)$ in the grid in different way in order to reduce rounding error for large n$.$

New Strategy: $(1)$ Introduce a new variable columnSum that is initialized as $0*$ in the outer loop, but before the inner loop. $(2)$ Replace mySum $=$ mySum $+$ F$($x$,$y$)$ in the inner loop with columnSum$=$columnSum $+$ F$($x$,$y$).(3)$ After the inner loop, but still inside the main loop, increment mySum: mySum$=$mySum$+$columnSum

Table $4$: Errors for your revised method of adding the numbers