Thread: 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. , and if they say that a given polynomial's degree is , they must choose so that .

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

Something here seems inconsistent to me.

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.

Thanks. I sort of figured this a while after posting, but your post confirmed my thoughts.