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旋转叠加与最小二乘法:奇异值分解(SVD)和四元数方法产生相同的结果。对G. 克内勒之前评论的回复。

Rotational superposition and least squares: the SVD and quaternions approaches yield identical results. Reply to the preceding comment by G. Kneller.

作者信息

Coutsias Evangelos A, Seok Chaok, Dill Ken A

机构信息

Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA.

出版信息

J Comput Chem. 2005 Nov 30;26(15):1663-5. doi: 10.1002/jcc.20316.

Abstract

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.

摘要

我们再次阐明,卡布斯方法和四元数方法在数学上是等效的方法,也就是说,它们包含相同的信息,并且在正确理解和应用时,对于任何关于最小二乘旋转叠加的问题,无论是通过适当旋转还是旋转反射,都会得出相同的答案。我们还给出了特征值谱的正确边界。

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