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This talk reviews differential equations on manifolds of matrices or tensors of low rank. They serve to approximate, in a low-rank format, large time-dependent matrices and tensors that are either given explicitly via their increments or are unknown solutions of differential equations. Furthermore, low-rank differential equations are used in novel algorithms for eigenvalue optimisation, for instance in robust-stability problems.
Christian Lubich (University of Tübingen)
Professor
Christian Lubich is the professor of numerical analysis at the University of Tübingen. He has made numerous contributions to the numerical solution of differential equations. Together with Ernst Hairer and Gerhard Wanner, he is the author of "Geometric Numerical Integration" (Springer, 2006), a leading text on structure-preserving ODE solvers.