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Numerische MathematikAbsolventInnen Seminar SS 21

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AbsolventInnen-Seminar • Numerische Mathematik

Dieses Semester wird das Seminar online auf Zoom stattfinden.

AbsolventInnen-Seminar
Verantwortliche Dozenten:
Prof. Dr. Tobias BreitenProf. Dr. Christian MehlProf. Dr. Volker Mehrmann
Koordination:
Ines Ahrens
Termine:
Do 10:00-12:00
Inhalt:
Vorträge von Bachelor- und Masterstudenten, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen
Sommersemester 2021 Vorläufige Terminplanung
Datum
Zeit
Vortragende(r)
Titel
Do 15.04.
10:15 Uhr
Vorbesprechung
Do 22.04.
10:15 Uhr
Do 29.04.
10:15 Uhr
Christian Mehl
Schur-like forms for matrices with symmetry structures in indefinite inner product spaces
Hermann Mena
Linear SPDEs: Simulation and Optimal Control
Do 06.05.
10:15 Uhr
Volker Mehrmann
Do 13.05.
10:15 Uhr
kein Seminar
Do 20.05.
10:15 Uhr
Matthias Voigt
Amon Lahr
Do 27.05.
10:15 Uhr
Philipp Krah
Eshwar Ramasetti
Do 03.06.
10:15 Uhr
Ines Ahrens
Do 10.06.
10:15 Uhr
Dorothea Hinsen
Paul Schwerdtner
Do 17.06.
10:15 Uhr
Karim Cherifi
Riccardo Morandin
Do 24.06.
10:15 Uhr
Tobias Breiten
Max Röger
Do 01.07.
10:15 Uhr
Marine Froidevaux
Damian Kołaczek
Do 08.07.
10:15 Uhr
Onkar Jadhav
Qiao Luo
Do 15.07.
10:15 Uhr
Philipp Schulze

Christian Mehl (TU Berlin)

Donnerstag, 29. April 2021

Schur-like forms for matrices with symmetry structures in indefinite inner product spaces

The Schur form of a Hermitian, skew-Hermitian, or unitary matrix is always diagonal. Unfortunately, this is no longer true if matrices that are selfadjoint, skew-adjoint, or unitary with respect to an indefinite inner product are considered. In this case, Schur-like forms, i.e. forms that display the eigenvalues and that are obtained under numerically stable transformation do not even always exist.

In this talk, we consider this problem for the case that the inner product is induced by a Hermitian and unitary matrix. The general result contains and combines two rather different, but well-known results from the literature on the existence of Hamiltonian Schur forms and on the diagonality of Schur forms of normal matrices.

Hermann Mena (TU Berlin)

Donnerstag, 29. April 2021

Linear SPDEs: Simulation and Optimal Control

We propose to solve linear stochastic partial differential equations by approximating the mean and covariance of the solution directly. As an illustration of our approach we present a numerical simulation of El Niño phenomena. El Niño is an irregularly periodical variation in winds and sea surface temperatures in the eastern equatorial Pacific ocean. We also consider  linear quadratic optimal control problems for this type of equations, i.e. the state equation is linear and the cost functional is quadratic. We show that the optimal control is given in feedback form in terms of a Riccati equation. We investigate the numerical approximation of the problem, in particular, the convergence of Riccati operators and the numerical solution of the optimal state. Numerical experiments show the performance of the proposed method.

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