Comments on the power method

In a recent short communication, Miyashita et al. have commented on the weakness of the NIPALS algorithm (equivalently the power method) for calculating the eigenvalues out of order. They offer a diagnostic to ascertain when this may have occurred and suggested a modification to the NIPALS algorithm to avoid this situation. Further comments regarding the use of the power method and Miyashita's presentation of its weakness are warranted. The general inadequacies of methods for decomposing a matrix with degenerate eigenvalues and their relationship to the orthogonal design of experiments are discussed.