Abstract
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.
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