Shah, Mili I.; Sorensen, Danny C. Best nonspherical symmetric low rank approximation. (English) Zbl 1201.65065 SIAM J. Matrix Anal. Appl. 31(2009), No. 3, 1019-1039 (2010). 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. Reviewer: Adhemar Bultheel (Leuven) Cited in 1 Document MSC: 65F20 Numerical solutions to overdetermined systems, pseudoinverses 92D20 Protein sequences, DNA sequences Keywords:singular value decomposition; symmetry; symmetry operation; symmetry constraints; rotation; reflection; dihedral; inversion; large scale; protein dynamics; low rank approximation; numerical examples Citations:Zbl 1124.65042 PDFBibTeX XMLCite \textit{M. I. Shah} and \textit{D. C. Sorensen}, SIAM J. Matrix Anal. Appl. 31, No. 3, 1019--1039 (2010; Zbl 1201.65065) Full Text: DOI