# Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations

Chahlaoui, Y and Gallivan, K.A and Van Dooren, P (2007) Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations. In: RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005. ESAIM: Proceedings, 20 . EDP Sciences, ESAIM, France, pp. 83-92.

We describe an algorithm for estimating the $\mathcal{H}_{\infty}$-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm uses Chandrasekhar iterations to obtain an estimate of the $\mathcal{H}_{\infty}$-norm and then uses extrapolation to improve these estimates.
Item Type: Book Section $\mathcal{H}_{\infty}$-norm, large sparse systems, Chandrasekhar iterations. MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theoryMSC 2010, the AMS's Mathematics Subject Classification > 49 Calculus of variations and optimal control; optimizationMSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysisMSC 2010, the AMS's Mathematics Subject Classification > 93 Systems theory; control Dr Younes Chahlaoui 01 Feb 2008 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/1019