Winter term 2017/18 was my first semester involved in teaching. Prof. Elisabeth Ullmann read a lecture on Introduction to Numerical Linear Algebra, and Laura Scarabosio, Jonas Latz, Konstantin Riedl, and me were making the tutorials discussing exercise sheets weekly.
The lecture was inspired by books of Bornemann (Numerische lineare Algebra, 2016) and Deuflhard (Numerische Mathematik I, 2002). We covered the four important topics:
- direct methods for linear systems (e.g. Gaussian elimination),
- error analysis,
- least squares,
- eigenvalue problems.
Additionally, we provided a possibility to get bonus points to improve final marks. The students had to solve five homeworks during the semester. Topics, accompanying the lecture, were
- Sherman-Morrison-Woodbury formula,
- Toeplitz matrices,
- iterative solution of linear system with Kaczmarz’s method,
- image deblurring with Tikhonov regularization,
- solution of the DoA (direction of arrival) problem with a singular value decomposition and a generalized eigenvalue problem.
In summer term 2018, it is continued by a lecture to numerics for ODEs.
I wish all the students great success in the final exams.