Max filtering with reflection groups

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 i...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 49; no. 6
Main Authors Mixon, Dustin G., Packer, Daniel
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2023
Springer Nature B.V
Subjects
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Euclidean geometry
Filtration
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Semidefinite programming
Subgroups
Visualization
Semidefinite programming
Reflection groups
Group invariance
Bilipschitz
Secondary: 51F15
42C15
Primary: 94A12
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Summary: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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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-023-10084-6