Least square function approximation

• Date: 23. 3. 2023
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Niel Van Buggenhout

A function of interest is sometimes only known from measurement, the available data is then a set of points and corresponding function evaluations in these points. From this data an approximation to the function can be computed, a powerful and well-known technique to do this is least squares approximation. Usually the least squares approximant is constructed from simple basis functions, for example polynomials or rational functions. A naive formulation of the least squares problem, i.e., finding the optimal approximant, leads to a system of equations with a Vandermonde matrix. Such a system is usually ill-conditioned. We discuss how, for any given set of points, a well-conditioned system of equations can be formulated by exploiting the connections between least squares problems, Krylov subspace methods and orthogonal polynomials. We also discuss how to efficiently update or downdate the least square approximant if data is added to or removed from the currently available data.