A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors

In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same expression as the Polar decomposition. We establish that the global convergence of our algorithm. Preliminary results show that the computational advantage of our algorithm. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.