This week, we will study orthogonal polynomials and their role in approximation theory, and specifically how a best approximation can be computed using these polynomials. We will see examples, such as Chebyshev and Legendre polynomials. While polynomials are a useful class of functions, they do have their limitations, and therefore we will start looking at rational approximations.

Intended Learning Outcomes

At the end of the week you should be able to:

  • explain the idea of orthogonal polynomials and their key properties;
  • know how to derive Legendre polynomials as orthogonal polynomials;
  • describe the rational approximation problem and the concept of Padé approximation.

Tasks and Materials

  • The second problem sheet is available and will be discussed this week, please have a look at it before class!