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Convergence of polynomial interpolation

  1. Apr 28, 2009 #1
    1. The problem statement, all variables and given/known data
    Let f be a contintuous real valued function on a closed interval [a, b]. The sup norm of such a function is maxx|f(x)|

    Let pn be a polynomial interpolation of f determined by n points [xi, f(xi)] where xi Ε [a, b] for every i.
    Suppose that the sequence {pn} is Cauchy with respect to the sup norm. Can you prove that pn --> f in sup norm? What can you say about this problem.

    2. Relevant equations

    3. The attempt at a solution
    Not yet given, I am unsure how to even approach this problem and was hoping someone had ideas?
  2. jcsd
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