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    Hi, The proof for finding the interpolation error bound of a function uses fourier series (which i am rusty with as i have not done them for 2 years).

    We basically found the H1 norm of our error ||u-u_h|| and said it is smaller than an interpolant error bound ||u - Iu|| where the interpolant is defined in the 1st screenshot.

    We have h_i = x_i - x_(i-1) (so h_i is the distance between each root)

    The start of the proof is what confused me, I do not understand the step to the equation at the bottom of the page, or why that is relevant. Can anyone help?

    Attached Images

    If you're talking about the final equation on the second slide, then they're using Parseval's equality/identity, I guess.
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Updated: January 10, 2015
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