One Modification which Increases Performance of N-Dimensional Rotation Matrix Generation Algorithm

Abstract

This article presents one modification of algorithm for generation of n-dimensional rotation matrix M, which rotates given n-dimensional vector X to the direction of given n-dimensional vector Y. Algorithm, named N-dimensional Rotation Matrix Generation Algorithm (NRMG) includes rotations of given vectors X and Y to the direction of coordinate axis x1 using two-dimensional rotations in coordinate planes. Proposed modification decreases the number of needed two-dimensional rotations to 2(Lw-1) were Lw is the number of corresponding components of the two given vectors, that are not equal.