A parallel algorithm for the unbalanced orthogonal Procrustes problem

In this paper, a new iterative algorithm is presented for approximating a solution for the orthogonal Procrustes problem min @[email protected]?"F with Q^TQ=I, where [email protected][email protected]?^l^x^m, [email protected][email protected]?^l^x^n and m>n. The new algorithm constructs a transformation Q by computing a sequence of plane rotations. Thus, it is simpler than the existing algorithms that use the recursive singular value decomposition updates, and can be efficiently implemented in a parallel environment. We give an analysis that shows how the new algorithm approximates the solution matrix Q and present an example for which the existing algorithm does not give the correct answer. Numerical experimental results show that the new algorithm has favorable convergence results. Finally we discuss the parallel implementation of the algorithm on a parallel architecture.