Interpolation

$($a$)$ Please implement functions

$p=$ ninterp$(nodevals,$ fvals$)$

$y=$polyeval$(p,x,$ nodevals$)$

where nodevals is the vector containing the interpolation nodes, fvals is the

vector containing function values at the nodes, and $p$ is a vector of Newton poly$-$

nomial coefficients and polyeval evaluates the Newton polynomial via Horner's

method to a whole list of points in the vector $x.$

$($b$)$ Now use your ninterp function to interpolate the two functions

$h_1(x)=e^{-x}+sinx$

$h_2(x)=\frac{1}{1+t^2}$

on the interval $-5,5$ for $n=4,8,12,$ and $16$ equidistant points. Plot both

interpolation polynomials with the functions they interpolate. Explain what you

see

Aside: If you want to declare a function which takes only one argument and

evaluates your specific Newton polynomial at any point to use when you plot,

you can do so in$-$line as follows.

poly $=$@$(x)polyeval(p,x,$ nodevals $)$

$x=$linspace$(-5,5,1000)$;

plot$(x,$poly$(x))$