On the computation of structured singular values and pseudospectra

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(n2 ) 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. Key words: Structured pseudospectrum, structured singular value, real perturbations, skew-symmetric perturbations, Hermitian perturbations, Hamiltonian perturbations.

• Type: Journal
• Year: 2010
• Where: SCL
• Authors: Michael Karow, Effrosini Kokiopoulou, Daniel Kressner
• Keywords: Hamiltonian Perturbations, SCL 2010, Singular Value, Structured