Quadrature-based Methods for Sylvester Equations

Abstract: The aim of this thesis is to investigate properties of quadrature-based methods to approximate a solution to the Sylvester equation AX + XBT = C. The Sylvester equation models large systems, hence the need for efficient numerical methods. The trapezoidal rule and Simpson’s rule, two classical methods, are implemented, as well as quadrature by Stenger. The results presented here shows the most promising method is quadrature by Stenger.