using python, $($b$)$ Evaluation

As discussed in class, we can write the interpolating polynomial as:

$p_n(x)=(x){\displaystyle \underset{j=0}{\overset{n}{}}}\frac{w_j*y_j}{(x-x_j)}.$

where

$(x)=(x-x_0)(x-x_1)cdots(x-x_n)$

$=pro{d}_i=0^n(x-x_i)$

$p_n(x)=\frac{{\displaystyle \underset{j=0}{\overset{n}{}}}\frac{w_j*y_j}{(x-x_j)}}{{\displaystyle \underset{j=0}{\overset{n}{}}}\frac{w_j}{(x-x_j)}}.$

where the term $(x)$ has been eliminated.

You may use either formulation.

def EvalLagr$($Z$,$ X$,$ Y$,$ w$)$:

$"""$

Evaluate the Lagrange Polynomial using the barycentric weights

Takes $4$ input parameters

$z$ array containing the points at which to evaluate the polynomial

$x$ containing the nodal points

$Y$ containing the function value at $x$

w barycentric weights

Returns the interpolating polynomial evaluated at the points $Z.$

$$

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return $PnZ$