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240036 Proseminar Angewandte Lineare Algebra (PS) (SoSe 2017)
Contents, comment
-
Es werden Themen behandelt, die in Vorlesungen zur Linearen Algebra oftmals
keinen Platz mehr finden, die aber für Anwendungen besonders relevant sind
und einen engen Bezug zur Analysis bzw. zur Numerischen Mathematik haben:- Grundlagen der Spektraltheorie: Schursche und Jordansche Normalform
- Singulärwertzerlegung
- Vektornormen und induzierte Matrixnormen
- Matrixkondition
- Gaußsches Eliminationsverfahren und LR-Zerlegung
- Cholesky-Zerlegung und QR-Algorithmus
- Jacobi-Verfahren und Gauß-Seidel-Verfahren
- Krylow-Unterraum-Verfahren
- Verfahren der konjugierten Gradienten
- Arnoldi-Verfahren und GMRES-Verfahren
- Lanczos-, Bi-Lanczos- und BiCG-Verfahren
- Least-squares und QR-Zerlegung mittels Householder Algorithmus
- Potenzmethode und orthogonale Iteration
- Jacobi-Verfahren für Eigenwerte
- Givens Householder Verfahren
Requirements for participation, required level
-
Lineare Algebra 1 + 2
Bibliography
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[1]: G. Allaire and S. M. Kaber. Numerical linear algebra, volume 55 of Texts in Applied Mathematics. Springer, New York, 2008. Translated from the 2002 French original by Karim Trabelsi.
[2]: G. H. Golub and C. F. Van Loan. Matrix computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD, fourth edition, 2013.
[3]: R. A. Horn and C. R. Johnson. Matrix analysis. Cambridge University Press, Cambridge, second edition, 2013.
[4]: A. Meister. Numerik linearer Gleichungssysteme. Friedr. Vieweg & Sohn, Braunschweig, 1999. Eine Einführung in moderne Verfahren. [An introduction to modern procedures].
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| Frequency | Weekday | Time | Format / Place | Period |
|---|
Subject assignments
| Module | Course | Requirements | |
|---|---|---|---|
| 24-B-GEO_ver1 Geometrie (Gym/Ge) | Proseminar | Study requirement
Ungraded examination |
Student information |
| 24-B-PX Praxismodul | Proseminar | Study requirement
Ungraded examination |
Student information |
| 24-E Ergänzungsmodul Mathematik | Proseminar | Study requirement
Ungraded examination |
Student information |
The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Mathematik (Gym/Ge als zweites U-Fach) / Master of Education | (Enrollment until SoSe 2014) | M.M.05 | Wahlpflicht | 3. | 3 | unbenotet |
- Registered number: 13
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- Last update basic details/teaching staff:
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