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Numerische Lineare Algebra - Lineare Gleichungssysteme und Matrixgleichungen SS 2013
Termine -
Inhalt -
Leistungsnachweise -
Literaturhinweise -
Handouts -
Übungsaufgaben -
Termine
| Vorlesung: |
Dienstags, |
07:30 - 09:00 (odd weeks) |
|
G02-106 |
|
|
Mittwochs, |
15:00 - 17:00 |
|
G22A-113 |
|
| Übung: |
Dienstags, |
07:30 - 09:00 (even weeks) |
|
G02-106 |
|
Inhalt
- Linear Systems:
- Direct solvers
- Stationary iterations
- Krylov methods (CG, MINRES,GMRES)
- Preconditioning (basic algorithms, saddle point examples)
- Multigrid
- Matrix equations:
- Introduction to matrix equations
- Direct solvers for linear matrix equations
- Low-rank solver for large-scale linear matrix equations
- Methods for algebraic Riccati equations
Literaturhinweise
Linear Systems:
- Trefethen, Bau, III.: Numerical Linear Algebra,
SIAM, Philadelphia, 1997.
- Elman, Silverster, Wathen: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, Oxford University Press, 2005.
- Saad: Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, 1996.
- Greenbaum: Iterative methods for solving linear systems, SIAM, Philadelphia, 1987.
- Meister: Numerik linearer Gleichungssysteme, Vieweg+Teubner, 2011.
Matrix Equations:
- B.N. Datta: Numerical Methods for linear Control Systems, Academic Press, 2003.
- A.C. Antoulas: Approximation of Large-scale Dynamical Systems, SIAM, 2005.
- Y. Zhou: Numerical Methods for Large-scale Matrix Equations with Applications in LTI System Model Reduktion, PhD Thesis, Rice University 2002.
- J. Saak: Efficient Numerical Solution of Large-scale Matrix Equations in PDE Control and Model Order Reduction, PhD Thesis, TU Chemnitz, 2009.
- G. Golub, C. Van Loan: Matrix Computations, 3. Aufl.,
The John Hopkins University Press, 1996.
- Petersen & Pederson: The Matrix Cookbook.
- K. Schäcke: On the Kronecker Product, 2004.
- M. Marcus & H. Minc: A Survey of Matrix Theory and Matrix inequalities, Allyn and Bacon, 1964.
Handouts
