Teaching Activities
Numerische Lineare Algebra - Lineare Gleichungssysteme und Matrixgleichungen WS2011/12
Termine
| Vorlesung: |
Montags, |
15:00 - 16:30 |
|
G22A-120 |
|
|
Donnerstags, |
11:00 - 12:30 |
|
G05-117 |
|
| Übung: |
Mittwochs |
11:10 - 12:40 |
|
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.
