Invited Address

RB McGee

Department of Mathematics & Statistics, Haverford College

Title: Orthogonal Polynomials in Scientific Computing

Abstract:

In linear algebra, we learn many benefits to finding a basis for a vector space, and when there is an orthogonal basis available it brings a smile to your face like a 50 degree day. When the vector space of interest is the collection of polynomials, we can apply the Gram-Schmidt process to the monomials and arrive at a basis of pairwise orthogonal polynomials. Interestingly, we also find that orthogonal polynomials arise through other means such as recurrence relations and as solutions of differential equations. In this talk, we will discuss popular families of orthogonal polynomials and look at how they help get to the root of fundamental tasks in scientific computing such as polynomial interpolation and numerical integration