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## 2008.5: Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations

2008.5: Y Chahlaoui, K.A Gallivan and P Van Dooren (2007) Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations. In: Mohammed-Najib Benbourhim, Patrick Chenin, Abdelhak Hassouni and Jean-Baptiste Hiriart-Urruty, (eds). RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005. ESAIM: Proceedings, 20. EDP Sciences, ESAIM, France, pp. 83-92.

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## Abstract

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 2000 > 15 Linear and multilinear algebra; matrix theoryMSC 2000 > 49 Calculus of variations and optimal control; optimizationMSC 2000 > 65 Numerical analysisMSC 2000 > 93 Systems theory; control 2008.5 Dr Younes Chahlaoui 01 February 2008