How to introduce an interpolation function into a neville's algorithm to solve a polynomial interpolation
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The question is:
interpolate f: [ 1, 1], f (x) = 1/(25x^2 + 1)
with a Lagrange polynomial at the equidistant points x_k = 1 + 2k/n, k = 0,...,n and plot the graph of pn for n = 10, 20, 40.
This is what I have so far
% plot out the n=10, 20, 40 polynomials which interpolate the
% function f(x) = 1/(25x^2+1) on the interval [-1,1] using
% equally spaced points
% function [yy]= nev[1/(25*xx.^2+1)];
xx = -1:0.1:1; % plot points in each case
% first plot the original function
yy = 1 ./ (25 * xx.^2 + 1);
plot(xx,yy);
hold on; % this makes the plots that follow pile up
for n = [10 20 40]
x = -1:2/n:1;
Q = 1 ./ (25 * x.^2 + 1); % get the interpolation points
for i = 1: 201
yy(i) = nev(xx(i), n, x, Q); %interpolate
end
plot(xx,yy);
end
hold off
But the function is not interpolating. What should the code be to get the desired graph?
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