Comments on ‘A structure-preserving method for the quaternion LU decomposition in quaternionic quantum theory’ by Minghui Wang and Wenhao Ma

Abstract

Claims were made in an article by Wang and Ma in 2013 that they had devised an algorithm for the quaternion LU decomposition that was significantly faster than the LU decomposition implemented in the Quaternion Toolbox for Matlab (QTFM). These claims have been tested and found to be unsupported by Matlab code supplied to the author by Wang and Ma. The author’s tests are presented, and test code made available as supplementary material. It is found that not only is the QTFM code faster, but that Wang and Ma’s algorithm has run-time that scales with the square of the size of the matrix, whereas the algorithm in QTFM has run time approximately linear in matrix size. These findings are consistent with an inspection of the code.