The Procrustes Problem for Orthogonal Kronecker Products
Adam W. Bojańczyk, Adam Lutoborski · SIAM Journal on Scientific Computing · 2003
The Procrustes problem for orthogonal Kronecker products is considered. Given matrices $A\in \mathbb{R}^{n^2\times k^2}$, $T\in \mathbb{R}^{n^2\times n^2},$ $n\ge k$, we minimize the Frobenius norm $\|T(Q\otimes Q)-A\|$ for all orthogonal Stiefel matrices $Q\in \mathbb{R}^{n\times k}$, $Q^TQ=I_{k}$. We introduce and implement left and right relaxation methods for minimization. Numerical results for the data in general and Kronecker product form are given to illustrate convergence of both methods.