Dieses Semester wird das Seminar online auf Zoom stattfinden.

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.

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.

• Absolveten Seminar WS 20/21
• Absolventen Seminar SS 20 
• Absolventen Seminar WS 19/20
• 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