how to approximate a function using Lagrange Interpolation?

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Otto 2012-11-24

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https://ww2.mathworks.cn/matlabcentral/answers/54694-how-to-approximate-a-function-using-lagrange-interpolation

Hi All,

I got an important question. It's desired to approximate the function f(x)=(x+sin(3*x))*(exp((-x^2)/4)) for the interval [-5 5].

It's a task and it's mandatory to approximate this function by Constructing a 25'th degree Lagrange polynomial. Using equally spaced data points is also required. The x-values of the first and last data points must be -5 and 5 respectively.

Here is the code:

That's the lagrange interpolation(I've written it myself):

function y = polyinterp(xNodes,yNodes,x)
n = length(xNodes);
y = zeros(size(x));
for k = 1:25
   w = ones(size(x)); 
   for j = [1:k-1 k+1:25] 
      w = (x-xNodes(j))./(xNodes(k)-xNodes(j)).*w;
   end
   y = y + w*yNodes(k);
end