Numerical Linear Algebra - Einzelansicht

This course will partially be taught in the e-learning format (1-2 weeks) in place of in-person instructions (remaining 12-13 weeks).

The code to register on moodle is nla.

There is no single textbook for the course. Possible references include:

[1] E. Darve and M. Wootters, Numerical Linear Algebra with Julia, vol. 172, SIAM, 2021.
[2] J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
[3] L. N. Trefethen and D. Bau, III., Numerical Linear Algebra, SIAM, Philadelphia, 1997.
[4] D. S. Watkins, Fundamentals of Matrix Computations, vol. 64, John Wiley, 2004.

This course requires a solid understanding of Linear Algebra, typically taught over two semesters with the second part sometimes called matrix theory, and of numerical methods (interpolation, rounding errors, Newton's method, numerical integration, and solving linear systems with Gaussian elimination).

There will be an in personal oral exam at the end of the term, if regulations permit. To qualify for the exam you have to achieve at least 50% of the points in the homework assignments.

The following topics, among others, will be covered in this course:

• solving linear systems and least squares problems, also for large and sparse systems,
• eigenvalue problems,
• singular value decomposition,
• Kronecker products and matrix equations, and
• their applications and more.

This course is aimed for students interested in numerical computations. Numerical linear algebra is at the core of many numerical algorithms, including, among others, PDE solvers, neural networks, and optimization. It forms the heart of the mathematics of the 21st century.

Für Studierende Mathematik Lehramt empfehlen wir die Lehrveranstaltung Numerik II, welche sehr ähnliche Themen behandelt. Aus diesem Grund kann Numerical linear algebra nicht länger für Mathematik Bachelor of Science angeboten werden.