Seminar Numerical Linear Algebra is a course for students interested in linear algebra and its numerical applications. The course aims to introduce master students to recent developments in the field of numerical linear algebra while the students improve their presentation skills.
Organizers
Sarah Gaaf and Gerard Sleijpen
Day, time and place
Mondays 11.15-13.00 in BBG 115, weekly from 11 February 2019 until 17 June 2019 (BBG 017 on Monday April 29).
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A preliminary list of topics is presented below. A list of papers on these topics will be available soon. Students are welcome to come up with a paper of their own interest within one of these subjects (in consultation with the teachers).
• Structured matrices: low rank and tensor formats.
• Matrix equations and differential matrix equations.
• Stochastic processes, networks and centrality.
• …
References
To give a flavor of the papers that might be studied, we list a few already below:
• D. Palitta e.a., Numerical methods for large-scale Lyapunov equations with symmetric banded data, 2018.
• D.F. Gleich e.a., Multilinear PageRank, 2015.
• F. Arrigo, e.a., Nonbacktracking walk centrality for directed networks, 2018.
• H. Bentbib e.a., Extended Krylov subspace methods for large-scale differential Sylvester matrix equations, 2018
• D. Kressner, e.a., Low-rank tensor Krylov subspace methods for parametrized linear systems, 2010
• …
Prerequisites
Students should be familiar with the contents of a first course in linear algebra. Knowledge of numerical methods and some programming experience (Matlab) is useful but not necessary.
Format
The seminar is aimed at MSc students with some background in linear algebra and scientific computing. Talks will be prepared and given by the participants, in close coordination with the organizers. Along with their talk speakers will also provide a handout and a (small) homework exercise for all participants, to be approved by the organizers. The speaker is responsible for grading this homework.
ECTS
7.5
Schedule
Second semester, block 3+4, 2 x 45 minutes per week
Language
English
Evaluation
Participants are expected to give two seminar talks (one with use of the blackboard, one with the use of slides), possibly more or less depending on the number of participants. They will study the material beforehand, hold a presentation about it, and distribute a hand-in exercise to the other seminar participants (to be approved beforehand by the seminar organizers and to be handed in by the students at the next lecture). The speaker is responsible for grading this hand-in exercise. In case of discussion about the solutions, the seminar organizers decide. Participants are expected to attend every seminar meeting. The final grade for the seminar is based on your talks and handouts (70%) and on your homework formulation and grades (30%).
Learning goals
After completion of the course, the student is able to:
• convert material from part of a graduate-level textbook or a scientific paper into a coherent and comprehensible presentation for fellow students and mathematicians in general,
• choose appropriate means of communicating theoretical mathematics to fellow students and mathematicians, in written and oral form,
• formulate and correct exercises that keep a balance between relevance, interest, and feasibility,
• explain specific topics from the content list of the seminar to fellow students, and put them in perspective as far as their relevance to wider mathematics is concerned.
Evaluation matrix
A preliminary grading scheme is presented below. This scheme might change a little. The final scheme will be communicated during the first lecture.
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Presentations |
Homework |
| Understanding the material |
30% |
0% |
| Effective communication of the material |
40% |
0% |
| Formulating and correcting homework |
0% |
10% |
| Homework grades |
0% |
20% |
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