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Math Help - Are the notes wrong?

  1. #1
    Senior Member
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    Are the notes wrong?

    I've highlighted parts of the image I'm concerned with:


    In other words, they want a cubic polynomial, i.e. P_3, and if they say that a given polynomial's degree is n+1, they must choose n=2 so that n+1=3.

    Perhaps they should have written the degree of the poly is n, not n+1?

    Something here seems inconsistent to me.
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  2. #2
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    There doesn't seem to be any inconsistency. You need to use the zeros of the (n+1)th degree Chebshev polynomial in order to get an n'th degree polynomial approximation for a given function f(x).

    Notice that a polynomial of degree n has n+1 coefficients (because of the constant term). You need to sample f(x) at n+1 points in order to get sufficient data to determine these coefficients. At the very simplest level, you need to sample the function at 2 points in order to get a straight line (i.e. degree 1) approximation for it.
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  3. #3
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    Thanks. I sort of figured this a while after posting, but your post confirmed my thoughts.
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