Browsing by Author "Lubich, Christian"
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- ItemGeometric Numerical Integration(Zürich : EMS Publ. House, 2016) Hairer, Ernst; Hochbruck, Marlis; Lubich, ChristianThe subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of numerical methods.
- ItemGeometric Numerical Integration(Zürich : EMS Publ. House, 2006) Hochbruck, Marlis; Iserles, Arieh; Lubich, ChristianThe subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how preserving the geometry affects the dynamical behaviour.
- ItemGeometric Numerical Integration(Zürich : EMS Publ. House, 2011) Hochbruck, Marlis; Iserles, Arieh; Lubich, ChristianThe subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of numerical methods.
- ItemGeometric Numerical Integration (hybrid meeting)(Zürich : EMS Publ. House, 2021) Lubich, Christian; McLachlan, Robert; Sanz-Serna, Jesús MaríaThe topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects.
- ItemLow rank differential equations for Hamiltonian matrix nearness problems(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Guglielmi, Nicola; Kressner, Daniel; Lubich, ChristianFor a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that some or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all eigenvalues lying off the imaginary axis, we look for a nearest Hamiltonian matrix that has a pair of imaginary eigenvalues. The Hamiltonian matrices can be allowed to be complex or restricted to be real. Such Hamiltonian matrix nearness problems are motivated by applications such as the analysis of passive control systems. They are closely related to the problem of determining extremal points of Hamiltonian pseudospectra. We obtain a characterization of optimal perturbations, which turn out to be of low rank and are attractive stationary points of low-rank differential equations that we derive. This permits us to give fast algorithms - which show quadratic convergence - for solving the considered Hamiltonian matrix nearness problems.