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.

Contents