Contents of the Seminar
We will discuss advanced research topics in geomathematics, more specifically inverse problems. After a brief recapitulation of the theory of linear inverse problems the non-linear case will be studied in greater detail.
- Illposed problems, operator equations, singular value decomposition.
- Regularization, filter, discrepancy principle, Tikhonov-Phillips regularization.
- Iterative methods, Landweber, conjugate gradients.
- Local illposedness, characterization of non-linear illposed problems.
- Non-linear Tikhonov-Phillips regularization, iterative methods, Newton method, non-linear Landweber method.
- Gauss-Newton methods, inexact Newton methods, convergence, regularization property.
- Projection methods, discretization, numerical examples.
Each participant will give a presentation on a chosen topic. Some topics are based on corresponding previous topics and require some coordination between the participants.
Organization of the Seminar
The presentations are given each week on Tuesday at 13:45 in 52-204 starting January 12, 2010.
The initial meeting takes place on Friday October 30th, at 13:30 in 49-506. Important date!!!
If you are interested, contact me. In particular if you cannot attend the aforementioned first meeting.
Link to
KIS entry.
Literature
- H. W. Engl, M. Hanke, A. Neubauer: Regularization of Inverse Problems. Kluwer Acad. Publ., 2000.
- A. Kirsch: An Introduction to the Mathematical Theory of
Inverse Problems. Springer, 1996.
- A. Rieder: Keine Probleme mit inversen Problemen. Vieweg, 2003.
- The lecture notes of last semester's lecture on inverse problems: Link
