Consider the Lagrange interpolating polynomial. Given input coordinates,

$!$

X $=($x$1,...,$ xn $)$ and corresponding function values

$!$

Y $=($y$1,...,$ yn $)=($ f $($x$1),...,$ f $($xn $)),$ the

Lagrange interpolant allows us to interpolate the function values at any point

$!$

x using

the formula:

$!$

P$($x$)=$ f $($x k

$)$Ln $"1,$ k$($x$),$

k$=1$

n

# where

$!$

Ln $"1,$k $($x$)=$ x $"$ x j

xk $"$ x j j $=1$

j #k

n

$ $.$ Note that the index

above runs from $1$ to n instead of $0$ to n that is used in the textbook. This is because

Matlab does not allow the index $0.$

The aim of this lab is to write a function for interpolation using Lagrange

Polynomials. We wish to write a function that will take

$!$

$($X$,$Y$)$ and a point

$!$

x as inputs

and return

$!$

P$($x$)$ as outp