Rotational superposition and least squares: the SVD and quaternions approaches yield identical results. Reply to the preceding comment by G. Kneller.
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.
Coutsias
Evangelos A
EA
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Seok
Chaok
C
Dill
Ken A
KA
D000465:Algorithms; D003198:Computer Simulation; D016018:Least-Squares Analysis; D008962:Models, Theoretical; D012399:Rotation