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.

#### 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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