1Polynomial interpolation
IB Numerical Analysis
1 Polynomial interpolation
Polynomials are nice. Writing down a polynomial of degree
n
involves only
n
+ 1
numbers. They are easy to evaluate, integrate and differentiate. So it would be
nice if we can approximate things with polynomials. For simplicity, we will only
deal with real polynomials.
Notation.
We write
P
n
[
x
] for the real linear vector space of polynomials (with
real coefficients) having degree n or less.
It is easy to show that dim(P
n
[x]) = n + 1.