This applet demonstrates the Runge-phenomen that appears when interpolating functions with polynomials. The function 

f(x)=  1 1+x2

is approximated in the interval [a,b]=[-5,5] using Newton interpolating polynomials, first with equally spaced nodes. Another approximation is based on Chebyshev nodes (not equally spaced) that are obtained by calculating 

xk=cos æ è (2n+1-2k)  p 2n+2 ö ø  b-a 2 +  a+b 2 ,      k=0,1,¼,n.

Compare these two approximations? What happens when increasing the degree n of the polynomials? 

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