
 Polynomial Interpolation 
  Given a continuous function f defined on the interval [1,1], and a set of n points (the nodes) in this interval, the (0,1,.....,m) HermiteFejér interpolation polynomial for f is the unique polynomial of degree (m+1)n1 which agrees with f at the nodes, and whose first m derivatives vanish at each node. 
  In the above figure, the nodes occur at the 8 points where the two graphs intersect at a horizontal point of inflection of the polynomial. 
  The graphs also suggest that for fixed m, the Lebesgue constant for (0,1,.....,2m) HF interpolation on the Chebyshev nodes is an increasing function of n, the number of nodes. 
 www.latrobe.edu.au /maths/smith/interp.html (708 words) 
