|This work deals with analysis of Kabsch and quaternion algorithms, which may be used for 3D superimposition of molecules by rigid roto-translation in computational chemistry and biology. Both algorithms, which are very im-portant for in silico drug design, were studied from the point of view of their non-trivial mathematical structure. Their computational complexity was in-vestigated by superimposition of various random pseudo-molecules with 2 – 100,000 atoms in Matlab. It was found that both proposed algorithm imple-mentations exhibit the same asymptotic time computational complexity of O(n), with the quaternion algorithm involving a higher number of floating-point operations (FLOPs) and showing lower computational performance in terms of serial CPU time.|
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