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On the computation of structured singular values and pseudospectra

by M. Karow and E. Kokiopoulou and D. Kressner

(Report number 2009-26)

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

@Techreport{KKK09_408,
  author = {M. Karow and E. Kokiopoulou and D. Kressner},
  title = {On the computation of structured singular values and pseudospectra},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-26},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-26.pdf },
  year = {2009}
}

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