The solution of orthogonal Procrustes problems for a family of orthogonally invariant norms (Q1895920)

The orthogonal Procrustes problem is considered. The intention is to find an orthogonal matrix that most nearly performs a transformation in the least squares sense. The problem arises in a variety of applications, and the solution in the Frobenius norm is not true in general. The paper deals with an important class of orthogonality invariant norms that contains the Frobenius norm as a special case. A method which retains orthogonality is discussed. It is shown that depending on the accuracy sought, the method can be effective. It is also shown that Newton's method provides a good enough result. Two examples are described. A comparison with the method which retains orthogonality is given.