We 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 $\eps$-pseudospectrum for a given $\eps$ and on the outer level we optimize over $\eps$, 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.

Computing extremal points of symplectic pseudospectra and solving symplectic matrix nearness problems.

GUGLIELMI, NICOLA;
2014

Abstract

We 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 $\eps$-pseudospectrum for a given $\eps$ and on the outer level we optimize over $\eps$, 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/16521
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