Browsing by Author "Mehrmann, Volker"
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- ItemFormal adjoints of linear DAE operators and their role in optimal control(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, VolkerFor regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.
- ItemLinear and Nonlinear Eigenproblems for PDEs(Zürich : EMS Publ. House, 2009) Mehrmann, Volker; Osborn, John; Xu, JinchaoThe workshop discussed the numerical solution of linear and nonlinear eigenvalue problems for partial differential equations. It included the theoretical analysis the development of new (adaptive) methods, the iterative solution of the algebraic problems as well as the application in many areas of science and engineering.
- ItemMini-Workshop: Dimensional Reduction of Large-Scale Systems(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2003) Mehrmann, Volker; Golub, Gene; Sorensen, Danny C.[no abstract available]
- ItemMini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control (hybrid meeting)(Zürich : EMS Publ. House, 2021) Mehrmann, Volker; Scherpen, Jacquelien M.A.; Schwenninger, Felix L.Dissipation of energy --- as well as its sibling the increase of entropy --- are fundamental facts inherent to any physical system. The concept of dissipativity has been extended to a more general system theoretic setting via port-Hamiltonian systems and this framework is a driver of innovations in many of areas of science and technology. The particular strength of the approach lies in the modularity of modeling, the strong geometric, analytic and algebraic properties and the very good approximation properties.
- ItemNichtnegative Matrizen, M-Matrizen und deren Verallgemeinerungen(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2000) Mehrmann, Volker; Schneider, Hans[no abstract available]
- ItemNumerical Solution of PDE Eigenvalue Problems(Zürich : EMS Publ. House, 2013) Mehrmann, Volker; Xu, JinchaoThis workshop brought together researchers from many different areas of numerical analysis, scientific computing and application areas, ranging from quantum mechanics, acoustic field computation to material science, working on eigenvalue problems for partial differential equations. Major challenges and new research directions were identified and the interdisciplinary cooperation was strengthened through a very lively workshop with many discussions.
- ItemSelf-adjoint differential-algebraic equations(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, Volker; Scholz, LenaMotivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value problem and show that it is associated with a self-conjugate operator and a self-adjoint pair of matrix functions. We then study general self-adjoint pairs of matrix valued functions and derive condensed forms under orthogonal congruence transformations that preserve the self-adjointness. We analyze the relationship between self-adjoint DAEs and Hamiltonian systems with symplectic flows. We also show how to extract self-adjoint and Hamiltonian reduced systems from derivative arrays.