PIMS- SFU CS Colloquium: Daan Huybrechs

  • Date: 03/09/2018
  • Time: 15:00
Daan Huybrechs, K.U. Leuven

Simon Fraser University


On the benefits of redundancy in the approximation of functions


Functions appearing in many applications, for example as the solution of an integral or differential equation, are usually discretized and approximated in a basis. Each function in a certain space can be uniquely represented in that basis. Correspondingly, the discretization of the equation at hand leads to a square linear system of equations, that has a unique solution and that is hopefully well-conditioned. Unfortunately, that ideal scenario is often difficult to realize. Indeed, there are many situations in which it is not straightforward to come up with a suitable basis in the first place: perhaps the function is defined on a complicated domain, or it is non-smooth, it has corner singularities or certain oscillatory behaviour. We show that a lot of flexibility is gained by relaxing the uniqueness condition of a basis, and by allowing some redundancy in the discretisation. This rapidly leads to ill-conditioned problems, since there is no longer a unique solution. However, we show this is easily remedied and we identify a rather general setting where redundancy is accompanied by numerically stable and efficient algorithms. This allows for a lot of creativity in the discretization of problems.

Other Information: 

SFU Big Data Hub
2:30 pm Reception (Atrium)
3:00 pm Lecture (Theatre, Rm. 10900)