2Orthogonal polynomials

IB Numerical Analysis

2 Orthogonal polynomials

It turns out the Chebyshev polynomials is just an example of a more general

class of polynomials, known as orthogonal polynomials. As in linear algebra, we

can define a scalar product on the space of polynomials, and then find a basis

of orthogonal polynomials of the vector space under this scalar product. We

shall show that each set of orthogonal polynomials has a three-term recurrence

relation, just like the Chebyshev polynomials.