Consider the function

f$($x$)=(1$ x

$2$

$)$ exp$($x

$2$

$)$

defined on the interval $[3,3]$ and interpolated using Chebyshev nodes and the Barycentric

formula. The answer for this question should be in the form of a matlab script.

$($a$)$ Plot the function f$($x$)$ on a dense grid $($e$.$g$.1000$ points$).[2]$

$[6]($b$)$ On the same figure plot the order N $=8$ Chebyshev nodes and the interpolant $($on the

same dense grid used in part a$).[$Hint: use the matlab function cheby.m from Avenue.$]$

$[4]($c$)$ By what factor does the interpolation error at the point x $=1\mathrm{.}05$ decrease when the

order is doubled, from N $=8$ to N $=16?$