# Jacob Westlund: An introduction to the QR-method

**Time: **
Mon 2019-01-28 14.30 - 15.30

**Location: ** Room 35, House 5, Kräftriket, Department of Mathematics, Stockholm University

**Respondent: **
Jacob Westlund

**Supervisor: **
Yishao Zhou

Abstract:*This thesis aims to provide an introduction to the QR-method, which is one of the most widely used algorithms for computing eigenvalues of matrices. The thesis starts by introducing fundamental concepts about matrices and eigenvalues which are then used as a theoretical framework throughout the thesis. In order to provide the reader with an understanding and a proof for the convergence of the QR-method, we introduce the Power method and show that the QR-method is equivalent to applying the Power method to multiple columns at the same time. We alsos how how the basic QR-method can be improved upon by reducing the initial matrix to Hessenberg form and by introducing shifts. Finally, we present the implicit QR-method, which is similar to the algorithms used in practice for computing eigenvalues.*