  We consider the problem of minimizing an objective function that depends on
an orthonormal matrix. This situation is encountered when looking for common
principal components, for example, and the Flury method is a popular approach.
However, the Flury method is not effective for higher dimensional problems. We
obtain several simple majorization-minizmation (MM) algorithms that provide
solutions to this problem and are effective in higher dimensions. We then use
simulated data to compare them with other approaches in terms of convergence
and computational time.
