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Faster and More Accurate Computation of the H Norm via Optimization

Benner, P., & Mitchell, T. (2018). Faster and More Accurate Computation of the H Norm via Optimization. SIAM Journal on Scientific Computing, 40(5), A3609-A3635. doi:10.1137/17M1137966.

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Genre: Journal Article

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© 2018, Society for Industrial and Applied Mathematics. This publication is with permission of the rights owner freely accessible on MPG.PuRe.
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Creators:
Benner, Peter1, Author
Mitchell, Tim1, Author
Affiliations:
1Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_1738141

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Free keywords: Mathematics, Optimization and Control, math.OC
Abstract: In this paper, we propose an improved method for computing the $\mathcal{H}_\infty$ norm of linear dynamical systems that results in a code that is often several times faster than existing methods. Our approach uses standard optimization tools to rebalance the work load of the standard algorithm due to Boyd, Balakrishnan, Bruinsma, and Steinbuch, with the aim of minimizing the number of expensive eigenvalue computations that must be performed. Unlike the standard algorithm, our improved approach can also calculate the $\mathcal{H}_\infty$ norm to full precision with little extra work, and also offers some opportunity to improve its performance via parallelization. Finally, our improved method is also applicable for approximating the $\mathcal{H}_\infty$ norm of large-scale systems.

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Dates: 2018
Publication Status: Published in print
Pages: -
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Rev. Type: Peer
Identifiers: DOI: 10.1137/17M1137966
arXiv: 1707.02497
URI: http://arxiv.org/abs/1707.02497
Other: pubdata_escidoc:2473910
Degree: -

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Title: SIAM Journal on Scientific Computing
Source Genre: Journal
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Pages: - Volume / Issue: 40 (5) Sequence Number: - Start / End Page: A3609 - A3635 Identifier: -