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Best nonspherical symmetric low rank approximation. (English) Zbl 1201.65065

An approximation to noisy data in \({\mathbb R}^3\) that have spatial symmetry can be obtained by a low rank approximation via singular value decomposition (SVD) that is invariant under the prescribed symmetry, i.e., a structure preserving SVD (SPSVD). The authors consider nonspherical symmetry groups.
First, a characterization of all the symmetry groups of interest in terms of at most three vectors (symmetry axes) characterizing their generators is given. This is essential to apply their previous SPSVD technique descibed by M. I. Shah and D. C. Sorensen [SIAM J. Matrix Anal. Appl. 28, No. 3, 749–769 (2006; Zbl 1124.65042)].
Then an algorithm is given to extract the symmetry groups underlying the data. This is obtained through an iterative reweighting process, which effectively removes outliers. Finally the proper SPSVD is described and applied to numerical examples in protein dynamics.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
92D20 Protein sequences, DNA sequences

Citations:

Zbl 1124.65042
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