Parallel implementations of Riemannian conjugate gradient methods for joint approximate diagonalization

We propose multi-threaded parallel implementations of the Riemannian conjugate gradient method (CG) on the Stiefel manifold and on the oblique manifold, suitable for solving two forms of the joint approximate diagonalization problem. In our implementations, each fundamental step of the method is explicitly modified and parallelized to enhance computational efficiency. Numerical experiments demonstrate that our modified CG implementations are more efficient than the original versions.