Solving Interpolation Error w/ ≤ 5*10-8 Precision

AI Thread Summary
The discussion focuses on determining the step size h for interpolating the function f(x)=cos(x) over the interval [0,π] to ensure that the interpolation error remains within ≤ 5*10-8. The user has calculated the third derivative f'''(x) and established that it is bounded by 1 in the specified interval. They are currently facing challenges in evaluating the expression |(x-xi+1)(x-xi)(x-xi-1)|, which is crucial for estimating the interpolation error. Assistance is requested to progress further in solving the problem. The user expresses gratitude for any help provided.
peripatein
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Hi,

Homework Statement


Interpolation for the function f(x)=cos(x) for evenly distributed values of x in [0,π] (h=xi+1-xi, xi=ih, i=0,1,...,πh) is carried out. Also known are f(xi).
I am asked to determine the value of h so that the interpolation's error is ≤ 5*10-8.

Homework Equations




The Attempt at a Solution


I have found f'''(x) for x in [0,π] to be ≤ 1.
Now I am stuck with evaluating |(x-xi+1)(x-xi)(x-xi-1)|.
I'd truly appreciate some assistance. Thanks in advance!
 
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I have managed on my own with this one. Thank you in any case :).
 

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