### Inverse Probleme (Winter Semester 2016/17)

- Lecturer: PD Dr. Frank Hettlich
- Classes: Lecture (0105100), Problem class (0105110)
- Weekly hours: 4+2

Schedule | |||
---|---|---|---|

Lecture: | Tuesday 14:00-15:30 | SR 3.68 | Begin: 18.10.2016 |

Wednesday 11:30-13:00 | SR 3.68 | ||

Problem class: | Thursday 15:45-17:15 | SR 3.61 | Begin: 27.10.2016 |

Lecturers | ||
---|---|---|

Lecturer | PD Dr. Frank Hettlich | |

Office hours: Wednesday 10:30am - 12am and on appointment | ||

Room 1.042 Kollegiengebäude Mathematik (20.30) | ||

Email: frank.hettlich@kit.edu | ||

Problem classes | Dr. Felix Hagemann | |

Office hours: | ||

Room 1.049 Kollegiengebäude Mathematik (20.30) | ||

Email: felix.hagemann@kit.edu |

Frequently questions in physics, technique or medicine lead to so called *inverse problems*. In general this means to reconstruct parameter of a given model from measurable data as it occurs for instance in computer tomography. Often these problems consist in seeking solutions of an ill-posed operator equation, i.e. an operator which does not have a bounded inverse.

The lecture will present the mathematical theory of linear ill-posed problems and will illustrated the phanomenon *ill-posed* by specific examples. We will introduce regularization methods for ill-posed problems as Tikhonov regularization. Furthermore also aspects of non-linear ill-posed problems will be discussed. This will be engross for instance by applications in tomography.

** Audience **

Students in the mathematical programs as of the 5th semester as well as interested students from physics or engineering siences. Necessary knowledge from functional analysis will be presented depending on the audience.

** Problem sheets **

The problem sheets and additional material will be posted on the Ilias homepage ... of the lecture.

# References

- H. Engel, M. Hanke and A. Neubauer,
*Regularization of Inverse Problems*, Kluwer Academic Publishers Group, Dordrecht, 1996. - A. Kirsch,
*An Introduction to the Mathematical Theory of Inverse Problems*(2nd ed.), Springer-Verlag, New York, 2011. - R. Kress,
*Linear Integral Equations*(2nd ed), Springer-Verlag, New York, 1999. - A. Rieder,
*Keine Probleme mit inversen Problemen*, F. Vieweg & Sohn, Braunschweig, 2003.