Develop a script that generates and evaluates a polynomial $p(x)$ of order $n-1$ in

barycentric form,

$p(x)=\frac{{\displaystyle \underset{k=1}{\overset{n}{}}}\frac{w_k{f}_k}{x-x_k}}{{\displaystyle \underset{k=1}{\overset{n}{}}}\frac{w_k}{x-x_k}},$

interpolating a given set of function values $f(x_k)=f_k=p(x_k)$ at a set of $n$ interpo$-$

lation nodes $x_1,$dots,$x_n$ with barycentric weights $w_k=(pro{d}_j=1,j{k}^n(x_k-x_j){)}^{-1}.$ The

interpolating polynomial $p$ is then evaluted at $m$ locations, ${}_l,l=1,$dots,$m.$

Write a MATLAB function that fills out the following template:

functioa pvals $=$ baryInterp$($xnodes$,$ fvala, $)$

$\%\%$ Barycentric polymonial interpolation

$7$ Generate and evaluate a polynonial, $p(x),$ that interpolates

$$ valuen in fvals at xnodes: xnodes $(i)$ vals$($i$)1=1,$dots,$n$

$x$ vhere $z=$ length$($fvalu$).$ To polynomial $p$ is evaluated at the

$\%x-$locations liated in $.p(x)$ bas order $n=1.$

$\%$ The barycestric form of the polynonial interpolant is used.

X Inputs: xnodes $-$ interpolation points

$\%$ fvals $-$ function values to be interpolated at moden

z $,x1-x-10$cations at vhich to evaleate the interpolast.

X Output: prals $-$ interpolating polynoaial evaluations at xi:

$\%$

pvals$($i$)=p((1)),1=1,$dots,$n$ where $=$ length $()$

$n=$ length$($fvals$)$; m$=$length $($xi$)$ ;

Refer to Gautsch, Section $2\mathrm{.}2\mathrm{.}5$ and the algotithm fragment $(2\mathrm{.}108)$ on p$.93.$ Also see Tre$-$

fetbot, Chapter $5.$ Extra style points will be awarded foe using a single one dimensional array

of length $n$ for $\{w_k\},($instead of the two dimensionsl arrays descibed in Cautschi asd Tre$-$

fethen$)$ and rescaling $\{w_k\}$ during the recunsion that generates it to avoid overflow$/$underflow$.$