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## Absolventen-Seminar • Numerische Mathematik

Verantwortliche Dozenten: | Prof. Dr. Christian Mehl, Prof. Dr. Volker Mehrmann |
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Koordination: | Ines Ahrens |

Termine: | Do 10:00-12:00 in MA 376 |

Inhalt: | Vorträge von Bachelor- und Masterstudenten, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen |

# Rückblick

- Absolventen Seminar SS 19
- Absolventen Seminar WS 18/19
- Absolventen Seminar SS 18
- Absolventen Seminar WS 17/18
- Absolventen Seminar SS 17
- Absolventen Seminar WS 16/17
- Absolventen Seminar SS 16
- Absolventen Seminar WS 15/16
- Absolventen Seminar SS 15
- Absolventen Seminar WS 14/15
- Absolventen Seminar SS 14
- Absolventen Seminar WS 13/14
- Absolventen Seminar SS 13
- Absolventen Seminar WS 12/13
- Absolventen Seminar SS 12
- Absolventen Seminar WS 11/12

### Rebekka Beddig (TU Berlin)

Donnerstag, 05. Dezember 2019

**H_2 x L_inf-optimal model reduction**

In this talk, we discuss H_2 x L_inf-optimal model reduction of parametric linear time-invariant systems. The H_2 x L_inf error is defined as the maximum H_2-error in the transfer function within a feasible parameter domain. We start with the computation of the H_2 x L_inf-norm using Chebychev interpolation. The next step is to minimize the error with nonsmooth constrained optimization. For the optimization process we use a gradient with respect to the matrix elements of the reduced order model. To obtain an asymptotically stable reduced system we include a stability constraint. Numerical experiments illustrate this method.

### Volker Mehrmann (TU Berlin)

Donnerstag, 28. November 2019

**Stability analysis of dissipative Hamiltonian differential-algebraic systems**

Port-Hamiltonian differential-algebraic systems are an important class of control systems that arise in all areas of science and engineering. When the system is linearized arround a stationary solution one gets a linear port-Hamiltonian differential-algebraic system. Despite the fact that the system looks very unstructured at first sight, it has remarkable properties. Stability and passivity are automatic, Jordan structures for purely imaginary eigenvalues, eigenvalues at infnity, and even singular blocks in the Kronecker canonical form are very restricted. We will show several results and then apply them to the brake squeal problem.

### Julianne Chung (TU Berlin)

Donnerstag, 14. November 2019

**Computational Methods for Large and Dynamic Inverse Problems**

In this talk, we describe efficient methods for uncertainty quantification for large, dynamic inverse problems. The first step is to compute a MAP estimate, and for this we describe efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization. These methods can address ill-posedness and can handle many realistic scenarios, such as in passive seismic tomography or dynamic photoacoustic tomography, where the underlying parameters of interest may change during the measurement procedure. The second step is to explore the posterior distribution via sampling. We use the generalized Golub-Kahan bidiagonalization to derive an approximation of the posterior covariance matrix for "free" and describe preconditioned Lanczos methods to efficiently generate samples from the posterior distribution.

### Matthias Chung (TU Berlin)

Donnerstag, 14. November 2019

**Sampled Limited Memory Methods for Least Squares Problems with Massive Data**

In this talk, we discuss massive least squares problems where the size of the forward model matrix exceeds the storage capabilities of computer memory or the data is simply not available all at once. We consider randomized row-action methods that can be used to approximate the solution. We introduce a sampled limited memory row-action method for least squares problems, where an approximation of the global curvature of the underlying least squares problem is used to speed up the initial convergence and to improve the accuracy of iterates. Our proposed methods can be applied to ill-posed inverse problem, where we establish sampled regularization parameter selection methods. Numerical experiments on very large superresolution and tomographic reconstruction examples demonstrate the efficiency of these sampled limited memory row-action methods.

### Onkar Jadhav (TU Berlin)

Donnerstag, 31. Oktober 2019

**Model order reduction for parametric high dimensional interest rate models in the analysis of financial risk**

The European Parliament has introduced regulations (No 1286/2014) on packaged retail investment and insurance products (PRIIPs). According to this regulation, PRIIP manufacturers must provide a key information document (KID) describing the risk and the possible returns of these products. The formation of a KID requires expensive valuations rising the need for efficient computations. To perform such valuations efficiently, we establish a model order reduction approach based on a proper orthogonal decomposition (POD) method. The study involves the computations of high dimensional parametric convection-diffusion reaction partial differential equations. POD requires to solve the high dimensional model at some parameter values to generate a reduced-order basis. We propose a greedy sampling technique for the selection of the sample parameter set that is analyzed, implemented, and tested on the industrial data. The results obtained for the numerical example of a floater with cap and floor under the Hull-White model indicate that the MOR approach works well for the short-rate models.

### Christian Mehl (TU Berlin)

Donnerstag, 31. Oktober 2019

**Distance problems for dissipative Hamiltonian pencils and related matrix polynomials **

We investigate the distance problems to singularity, higher index, and instability for dissipative Hamiltonian systems by developing a general framework for matrix polynomials with a special symmetry and positivity structure. As we will show, the mentioned distances can then be formulated as the distance to a common kernel of some of the coefficients of the given matrix polynomial.

### Paula Klimczok (TU Berlin)

Donnerstag, 24. Oktober 2019

**Classification of Two-Variable Linear Differential Equations with Large Delays**

In this talk we will discuss the stability of linear differential equations of the form x’(t)=Ax(t)+Bx(t−τ) with a discrete delay τ and constant A and B. For a large delay τ the eigenvalues can be approximated by two sets: the asymptotic strongly unstable spectrum and the asymptotic continuous spectrum. We will characterise these sets in the case of A, B ∈ R^{2×2} and give conditions for the stability. Further, we will take a look on the computation of the eigenvalues.