Numerical linear algebra - Einzelansicht

You should have done at least one course in Numerical Analysis and Programming (Numerik 1).

Criteria for getting a course assessment:

oral exam at the end of the semester

Students should learn a range of modern iterative methods for solving linear systems and for solving eigenvalue problems. They should be able to analyse their algorithms and should have an understanding of relevant practical issues.

Topics will be chosen from the following:

Linear matrix eigenvalue problem: The Schur form. The power method and its extensions. Subspace methods. Error analysis and convergence theory. Perturbation theory. Givens/Householder QR factorization and the QR method. The Lanczos method and extensions. Krylov subspace methods. The Jacobi algorithm. The Divide and Conquer method. Extensions to generalised and nonlinear eigenvalue problems. Special matrix classes and applications. The Singular Value Decomposition and applications.

Iterative methods for linear systems: Convergence of stationary iteration methods. Descent methods and the conjugate gradient method and extensions. Krylov subspace methods and preconditioners. Relationship between Lanczos and conjugate gradient method. Error bounds and perturbation theory. Convergence and extensions. Special matrix classes and applications.

BSc Mathematics

MSc Mathematics

MSc Data Science

MSc Computational Science

MEd and BEd Mathematics