# Ernst Cederholm: Kontrollteoretiska ri-funktioner

BSc thesis presentation

**Time: **
Tue 2020-06-02 09.00 - 10.00

**Location: **
Zoom, meeting ID: 668 5477 8417

**Lecturer: **
Ernst Cederholm

**Supervisor: **
Yishao Zhou

### Abstract

Spline functions are an important tool when it comes to approximation of data. Magnus Egerstedt and Clyde Martin demonstrated in Control Theoretic Splines how interpolating and smoothing splines can be integrated with the theory of linear systems. This thesis includes a mathematcical background that is sufficient to reconstruct several of their results, including spline functions on the Cartesian plane and on the unit sphere. Egerstedt and Martin demonstrated that the optimal and smooth spline functions converge as the amount of data grows. In this thesis, an error in their proposed limit function was found and corrected.