Computing spectral value sets using the subharmonicity of the norm of rational matrices

Spectral value sets (SVS) are structured versions of pseudospectra, a tool of matrix analysis that has been popularized by Trefethen and Godunov in recent years. The main result contained in this note is a new algorithm for calculating complex SVS which, using the subharmonicity of the norm of rational matrices, is able to save large amounts of computation whenever the initial set of interest Ω₀⊂ℂ is larger than the actual size of the SVS to be visualized. The algorithm, as a result of a corrector step, is also able to recover the subsets of the SVS which are not contained in Ω₀. Numerical examples are discussed which illustrate the advantages of the new method. This work has been financially supported by the Deutscher Akademischer Austauschdienst.