A MONOTONICALLY CONVERGENT ALGORITHM FOR ORTHOGONAL CONGRUENCE ROTATION

Brokken has proposed a method for orthogonal rotation of one matrix su ch that its columns have a maximal sum of congruences with the columns of a target matrix. This method employs an algorithm for which conver gence from every starting point is not guaranteed. In the present pape r, an iterative majorization algorithm is proposed which is guaranteed to converge from every starting point. Specifically, it is proven tha t the function value converges monotonically, and that the difference between subsequent iterates converges to zero. In addition to the bett er convergence properties, another advantage of the present algorithm over Brokken's one is that it is easier to program. The algorithms are compared on 80 simulated data sets, and it turned out that the new al gorithm performed well in all cases, whereas Brokken's algorithm faile d in almost half the cases. The derivation of the algorithm is given i n full detail because it involves a series of inequalities that can be of use to derive similar algorithms in different contexts.