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

Chahlaoui, Younes and Gallivan, Kyle and Paul, Dooren (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, ESAIM, pp. 83-92.

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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.