1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Interpolation polynomials and errors.

  1. Nov 1, 2013 #1
    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted