Eigenvalue Problems: Unterschied zwischen den Versionen
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*<s>Übungen ausarbeiten?</s> |
*<s>Übungen ausarbeiten?</s> |
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| − | = |
+ | =Themen= |
| + | ==Motivation and Basics== |
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| − | *Einführung, Begriffe, SVD |
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| + | ===Motivation=== |
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| − | **komplex, hermitisch, verallgemeinert,.... |
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| + | (siehe Saad) [Chris] |
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| − | *Traditionelle Solver: Jacobi, QR, Householder |
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| + | *Mech Vibrations |
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| + | *Electrical Network |
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| + | *Stability |
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| + | *Macro-Econimics |
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| + | *Markov |
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| + | *... |
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| + | |||
| + | ===Basics=== |
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| + | [Chris] |
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| + | *Classification Std/Gen/Poly/N.lin |
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| + | *Classification ASYM/SYM/HERM/POSDEF |
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| + | **Definition |
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| + | **Properties of Spectrum |
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| + | *Dense/Sparse |
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| + | *MinMax (P206,S30) |
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| + | *... (see literature) |
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| + | |||
| + | ==Full Solvers== |
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| + | [Michi/Ralf] |
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| + | *Definition |
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| + | *LDU/LDL/LL |
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| + | *GramSchmidt/QR/tridiag?/Givens (P151) |
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| + | *Reduction to tridiag (P125) |
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| + | *Jacobi(P189/Sormann) |
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| + | *Householder? |
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| + | |||
| + | ==Sparse Solvers== |
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| + | [Michi] |
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*Power Method |
*Power Method |
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| + | *PINVIT |
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| − | *Krylov Raum, Lanczos, Arnoldi |
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| + | *Rayleigh Quotient |
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| − | *Band/Block-Lanczos |
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| + | *Krylov/Ritz Vals/Vecs |
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| − | *Orthogonlisierung (local, full, SO, neue Methode) |
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| + | *Arnoldi |
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| − | *Implicitly Restarted |
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| + | *Lanczos |
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| − | *AMLS |
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| + | *Band/Block Lanczos |
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| − | *Davidson-Liu? Jacobi-Davidson? |
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| + | [Ralf] |
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| − | *Parallesierung/CPU |
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| + | *Orthofgonalisierung |
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| + | **Full |
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| + | **SO |
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| + | **... |
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| + | *Davidson-Liu |
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| + | *Jacobi-Davidson |
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| + | |||
| + | |||
| + | ==Preconditioning== |
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| + | [Chris] |
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| + | *Shift+Invert |
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| + | *Condition number |
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| + | *Klatsch |
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| + | |||
| + | |||
| + | ==Non-standard EVP== |
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| + | [Chris] |
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| + | *Def: Gen/quad/Poly/NLIN |
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| + | *Transformations |
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| + | *Solvers |
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| + | |||
| + | ==Applications== |
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| + | *Model Order reduction/Electro.. [Chris] |
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| + | *AMLS [Ralf] |
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| + | *Multigrid [Ralf] |
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| + | *many body ph. [Michi] |
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| + | |||
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Version vom 29. Oktober 2009, 12:45 Uhr
- Workshop im Rahmen des DKs
- Vortragende
- Ralf Gamillscheg
- Christian Scheiber
- Michael Knap
Gerhard Unger
auch Übungen
Inhaltsverzeichnis
mögliche Zeiteinteilung
- Termin: ab 18.1.2009
- Umfang: 9h
- 3 Tage a 3h, nachmittags
- jeweils 2h+pause+1h
Aufgaben
- Themen finden
- Themen aufteilen
- Ausarbeiten
Übungen ausarbeiten?
Themen
Motivation and Basics
Motivation
(siehe Saad) [Chris]
- Mech Vibrations
- Electrical Network
- Stability
- Macro-Econimics
- Markov
- ...
Basics
[Chris]
- Classification Std/Gen/Poly/N.lin
- Classification ASYM/SYM/HERM/POSDEF
- Definition
- Properties of Spectrum
- Dense/Sparse
- MinMax (P206,S30)
- ... (see literature)
Full Solvers
[Michi/Ralf]
- Definition
- LDU/LDL/LL
- GramSchmidt/QR/tridiag?/Givens (P151)
- Reduction to tridiag (P125)
- Jacobi(P189/Sormann)
- Householder?
Sparse Solvers
[Michi]
- Power Method
- PINVIT
- Rayleigh Quotient
- Krylov/Ritz Vals/Vecs
- Arnoldi
- Lanczos
- Band/Block Lanczos
[Ralf]
- Orthofgonalisierung
- Full
- SO
- ...
- Davidson-Liu
- Jacobi-Davidson
Preconditioning
[Chris]
- Shift+Invert
- Condition number
- Klatsch
Non-standard EVP
[Chris]
- Def: Gen/quad/Poly/NLIN
- Transformations
- Solvers
Applications
- Model Order reduction/Electro.. [Chris]
- AMLS [Ralf]
- Multigrid [Ralf]
- many body ph. [Michi]
nächstes Treffen
- In der Woche vom 26.10.
Abwesenheiten
- Michi 4.-19.10.
- Ralf 14.12. - 22.12.
- Chris bis 19.10. / 21.11.-1.12.
Besprechung 16.9.2009
Grobeinteilung der Themen
Link zur Mindmap, Media:090916mindmap.pdf
Links
- http://www.sam.math.ethz.ch/~kressner/zss/
- Templates for Eigenvalue Problems Online Buch http://www.cs.utk.edu/~dongarra/etemplates/index.html
- ETH Diss http://itp.tugraz.at/~ralfgam/download/ETH-EigenvalueDiss.pdf
Anmerkungen
- Kressner Matlab skripte vorführen
- Systematische Einteilung langsam Aufbauen
- Welcher Algorithmus für was?
- Einführung mit prakt. Beispielen
