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.