Guglielmi, NicolaKressner, DanielLubich, Christian2015-02-202015-02-202015-02-20201410.1137/13094476Xhttps://infoscience.epfl.ch/handle/20.500.14299/111175WOS:000346843200009We study differential equations that lead to extremal points in symplectic pseudospectra. In a two-level approach, where on the inner level we compute extremizers of the symplectic epsilon-pseudospectrum for a given epsilon and on the outer level we optimize over epsilon, this is used to solve symplectic matrix nearness problems such as the following: For a symplectic matrix with eigenvalues of unit modulus, we aim to determine the nearest complex symplectic matrix such that some or all eigenvalues leave the complex unit circle. Conversely, for a symplectic matrix with all eigenvalues lying off the unit circle, we consider the problem of computing the nearest symplectic matrix that has an eigenvalue on the unit circle.symplectic pseudospectrumdistance to instabilitylow-rank dynamicsdifferential equations on Stiefel manifoldstext::journal::journal article::research article