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Interpolation polynomials and errors.

  1. Nov 1, 2013 #1
    Hi,
    1. The problem statement, all variables and given/known data
    A quadratic piecewise interpolation is carried out for the function f(x)=cos(πx) for evenly distributed nodes in [0,1] (h=xi+1-xi, xi=ih, i=0,1,...,πh).
    I am asked to bound the error.

    2. Relevant equations



    3. The attempt at a solution
    I believe the error in this case is bounded thus:
    |e(x)| ≤ [1/(n+1)!]max(f(n+1)(c))*max(∏[i=0,n](x-xi))
    where c[itex]\in[/itex][0,1]
    hence, yielding [1/3!]*π3*2h3/(3√3)
    (1) First of all, is that correct?
    (2) Next, in case this is correct, why is it bounded thus instead of as in the case for f(x)=e-x in [0,1] where, generally, it is bounded thus:
    |e(x)| ≤ hn+1/(4*(n+1))
    ??
    I'd sincerely appreciate some insight, please.
     
    Last edited: Nov 2, 2013
  2. jcsd
  3. Nov 2, 2013 #2
    Was this posted to the wrong group?
     
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