Abstract
Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of minimum distortion in the setting where G is a reflection group. Our analysis involves an interplay between Coxeter’s classification and semidefinite programming.
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Acknowledgements
The authors thank Jameson Cahill, Dan Edidin, Joey Iverson, John Jasper, and Yousef Qaddura for enlightening discussions, Ben Blum-Smith for helping us simplify our proof of Lemma 5, and the anonymous referee for various comments and suggestions that improved the presentation of our results.
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Communicated by: Felix Krahmer
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Mixon, D.G., Packer, D. Max filtering with reflection groups. Adv Comput Math 49, 82 (2023). https://doi.org/10.1007/s10444-023-10084-6
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DOI: https://doi.org/10.1007/s10444-023-10084-6