an:07006500
Zbl 1405.93028
Benner, Peter; Lowe, Ryan; Voigt, Matthias
\(\mathcal{L}_{\infty}\)-norm computation for large-scale descriptor systems using structured iterative eigensolvers
EN
Numer. Algebra Control Optim. 8, No. 1, 119-133 (2018).
2155-3289 2155-3297
2018
j
93A15 93B40 15A22 93-04 93C05 93B55 93B60 93C15
Arnoldi methods; descriptor systems; dominant poles; even matrix pencils; \(\mathcal{L}_\infty\)-norm
Summary: In this article, we discuss a method for computing the \(\mathcal{L}_\infty\)-norm for transfer functions of 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 \(\mathcal{L}_\infty\)-norm. Finally, we compare our method to a previously developed algorithm using pseudopole sets. Numerical examples demonstrate the reliability and accuracy of the new method along with a significant drop in the runtime.