Advanced Numerical Linear Algebra

What it is about

In this module you will learn methods of numerical linear algebra with applications in data assimilation, model reduction and the solution of matrix equations. In the end you will be able to formulate and interpret variational and statistical data assimilation problems, understand and implement common model reduction procedures for linear systems, and apply theory and numerical methods for Lyapunov and Sylvester equations.

What you will be able to do

• Construction and analysis of variational data assimilation problems
• Analysis and interpretation of statistical filter methods
• Understanding and implementation of Balanced Truncation
• Understanding rational interpolation (Moment Matching, IRKA)
• Theory of existence and uniqueness of matrix equations
• Knowledge of direct and iterative methods for Lyapunov and Sylvester equations
• Familiarity with the Bartels-Stewart algorithm and projection methods for large problems

What the module consists of

• VorlesungPresentation of theoretical foundations and examples; motivation for independent in-depth study
• ÜbungAccompanying practical exercises to deepen understanding
• Hausaufgaben / SelbststudiumExercise sheets and model solutions for self-check and deepening
• Programmierung mit MATLABPractical implementation and execution of the methods

Teaching method

• Vortrag mit BeispielenDelivery of learning content and discussion with students
• Übungsaufgaben mit MusterlösungenDeepening of understanding and self-monitoring of learning progress
• Selbstständige Analyse und LiteraturarbeitPromotion of autonomous in-depth study of relevant scholarly literature