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 Prof. : Klaus Diepold Teaching Assistants: Sven Gronauer, Simon Schumann Contact tvsc.ldv@xcit.tum.de Target Group: Master level students in technical fields ECTS: 6 Credits Contact Hours: 3 SWS Turnus: Winter term Registration: via TUMOnline (necessary to get access to course materials on Moodle) Time & Place: Wednesdays, 09:45-12:15, Room Z995 Start: October 18th, 2023

## Registration and Prerequisites

• No pre-registration necessary
• Working knowledge of (Numerical) Linear Algebra and Matlab.

## Contents

A broad range of engineering problems involve the solution of large systems of linear equation or other linear algebra computations involving large matrices. This includes finding the best  search result using Google’s “PageRank” technology to designing large-scale integrated semiconductor circuits. Other signal processing tasks can also be represented in this way. We mostly assume the linear systems to be time-invariant. This assumption enables us to use traditional tools in system modeling such as computing the response of a system in the frequency-domain (using FFTs) or using the z-transform.

However, there are systems where the property of time-invariance is not satisfied and where frequency-domain operations are no longer feasible.  The purpose of this course is to introduce an alternative way to treat linear systems that generalizes also to time-varying systems. Linear Systems will be described in terms of a state-space realization, which uses concepts of linear algebra. The course emphasizes the representation of large-scale computational problems (matrix-vector multiplication, matrix inversion, matrix factorization, etc.) as problems of time-varying linear systems. This approach allows that engineers can apply linear system based thinking to design fast and efficient numerical algorithms for large-scale linear algebra problems.

Students will work in teams on project tasks, developing Matlab using the techniques covered in the class. The course will instruct students to work in an agile work style to software development supported by modern, state-of-the-art software tools.

Reference Literature:

• P. Dewilde, K. Diepold, A.-J. van der Veen. Systems and Computations. 2018. Preprint available on Moodle.
• P. Dewilde, A.-J. van der Veen. Time-Varying Systems and Computations. Kluwer Academic Publishers, 1998.

The background mathematical knowledge (also covered in exercise) is available in:

• G. Strang. Linear Algebra and its Applications. Hartcourt Brace Jovanovich Publishers, San Diego, 1988.