Use Neville\'s Method to obtain the approximations for Lagrange interpolating po

Question

Use Neville's Method to obtain the approximations for Lagrange interpolating polynomials of degrees one, two, and three to approximate the following:

f(0.43) if

f(0)=1,

f(0.25)=1.64872

f(0.5)=2.71828

f(0.75)=4.48169

Explanation / Answer

I wrote a matlab code which is attached. got the following results : n=1 , polynomial degree 1 ----> y=2.1158 n=2 , polynomial degree 2 ----> y=2.3764 n=3 , polynomial degree 3 ----> y=2.3606 MATLAB Code is here : ------------------------------------------------ clc clear all n=3 % degree of plynomial % data points x=[0 0.25 0.5 0.75]; y=[1 1.64872 2.71828 4.48169]; % place where interpolation is needed xx=0.43 for i = n:-1:1 for j = 1:i y(j) = (xx-x(j))*y(j+1) - (xx-x(j+n+1-i))*y(j); y(j) = y(j)/(x(j+n+1-i)-x(j)); end end y=y(1) ---------------------------------------------------

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