L∞-norm computation for large-scale descriptor systems using structured iterative eigensolvers / Ryan Lowe, Matthias Voigt

Abstract

Abstract: In this report, we implement a method of computing L∞-norms for descriptor systems using structured iterative eigensolvers. In particular, the algorithm computes some desired imaginary eigenvalues of an even matrix pencil and uses them to determine an upper and lower bound to the L∞-norm. We finally compare our method to a previously developed algorithm using structured pseudospectra. Numerical examples demonstrate the reliability and accuracy of the new method along with a significant drop in the runtime.