# Are the notes wrong?

• Jul 28th 2009, 03:46 AM
scorpion007
Are the notes wrong?
I've highlighted parts of the image I'm concerned with:
http://img166.imageshack.us/img166/2306/math8.png

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

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

Something here seems inconsistent to me.
• Jul 28th 2009, 10:47 AM
Opalg
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.
• Jul 28th 2009, 04:44 PM
scorpion007
Thanks. I sort of figured this a while after posting, but your post confirmed my thoughts.