Report 2009-26

On the computation of structured singular values and pseudospectra

M. Karow, E. Kokiopoulou and D. Kressner

Abstract: Structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations. This paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalue minimization characterization, including the classes of real, skew-symmetric, Hermitian, and Hamiltonian perturbations. For all these structures we develop algorithms that require O(n^2) operations per grid point, combining the Schur decomposition with a Lanczos method. These algorithms form the basis of a graphical Matlab interface for plotting structured pseudospectra.

Keywords: Structured pseudospectrum, structured singular value, real perturbations, skew-symmetric perturbations, Hermitian perturbations, Hamiltonian perturbations

Paper: Available as PDF (694KB) or as hardcopy to order reports@sam.math.ethz.ch.