### Inverse Probleme (Winter Semester 2020/21)

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

The lecture will be given online asynchronously and the problem session online synchronously. All information and material for the course are collected on the Ilias page of the lecture.

Schedule | |||
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Lecture: | Wednesday | Online | Begin: 4.11.2020 |

Friday | Online | ||

Problem class: | Monday 12:00-13:30 | Online | Begin: 9.11.2020 |

Lecturers | ||
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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 | M.Sc. Marvin Knöller | |

Office hours: by appointment | ||

Room 1.038 Kollegiengebäude Mathematik (20.30) | ||

Email: marvin.knoeller@kit.edu |

Frequently, problems from natural sciences, technics, or medicine lead to so called inverse problems. In general it means to recover information on parameter of a given model from observable data for instance as in computer tomography. Often these problems can be formulated as seeking a solution of an ill-posed operator equation, that is an operator which do not allow for a continuous inverse.

The lecture will cover the mathematical theory of linear ill-posed problems and will illustrated the phenomenon of "ill posedness" by some examples. We will present regularization methods for ill-posed problems like the Tikhonov regularization. Additionally, some aspects from nonlinear ill-posed problems will be discussed.

** Audience**

Students of the mathematical programs as from third year, as well as interested students from physics or engineering sciences. The required knowledge from functional analysis will be covered in the lecture as suitable for the audience

# 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.