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Question

Let 

class="katex-mathml">f(x)=1+x21

Interpolate f(x) on the interval [-5,5] with Lagrange polynomials of degree n, Pn(x), which agree with f at n+1 equally spaced points on the interval. Do this for n=5, 10, 15, 20. Explain what method you are using to compute the polynomials. You may use matlab commands polyval and polyfit.


Plot P5(x), P10(x), and P15(x) separately, but with each f(x). (When displaying a graph, plot the points xi,yi where xi-xi-1 = 0.01)


Compute the error at the point q=1+(10) for each of the approximations. What would you expect to happen as n gets larger? What is actually happening?

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