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Rotational superposition and least squares: The SVD and quaternions approaches yield identical results. Reply to the preceding comment by G. Kneller
Author(s) -
Coutsias Evangelos A.,
Seok Chaok,
Dill Ken A.
Publication year - 2005
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20316
Subject(s) - quaternion , superposition principle , least squares function approximation , rotation (mathematics) , mathematics , eigenvalues and eigenvectors , yield (engineering) , spectrum (functional analysis) , singular value decomposition , mathematical analysis , algorithm , physics , geometry , statistics , quantum mechanics , thermodynamics , estimator
We clarify once again that Kabsch's method and the Quaternion method are mathematically equivalent methods, that is, that they contain identical information and, when properly understood and applied, lead to identical answers to any questions regarding least‐squares rotational superposition, either by proper rotations or by rotation‐reflections. We also provide the correct bounds for the eigenvalue spectrum. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 1663–1665, 2005