Semester:

FS 2022 
Type:

Seminar 
Lecturer:


Links:

KSL 
The theme of this seminar will be Numerical Linear Algebra. We will start with a few lectures introducing important fundamentals. The core part of the seminar will then consist of presentations by the participants on individually assigned topics. Throughout the semester we will additionally include programming exercises in C++ such that all participants will develop a solid practical understanding of the covered methods.
Numerical Linear Algebra provides all essential tools to the numerical scientists, those using vectors and matrices. Those tools consist of practical algorithms with a design relying on functional analysis. This form of applied linear algebra is ubiquitous in the engineering world. However, although broadly used, few scientists know the tricks of modern linear algebra systems.
This seminar course is designed to reveal the secrets of the important methods:
 QR factorization: (modified) GramSchmidt orthogonalization and Householder reflectors
 LU decomposition: Gaussian elimination, pivoting and Cholesky factorization
 Eigenvalues: Power iteration, Inverse iteration, QR algorithms and generalization
 Iterative methods: Krylov methods (conjugate gradients), convergence, preconditioning and generalization