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by Zhenlong Hu and 3 other authors View PDFHTML (experimental) Abstract: Owing to the effectiveness of Tensor Train (TT) decomposition in managing high-order tensors， Defeng Sun， we leverage the left-orthogonal property of the TT-decomposition to construct a novel quotient manifold and introduce a family of admissible Riemannian metrics. Within this geometric framework， [Submitted on 29 Jun 2026] Title: Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry Authors: Zhenlong Hu， Zhongming Chen， realized via two novel retractions based on recursive polar and QR decompositions that respect the recursive orthogonalization structure of the TT format. We then derive Riemannian gradient descent and conjugate gradient methods to solve the tensor completion problem. Theoretically， thereby enhancing computational efficiency over conventional quotient-based methods. Numerical experiments demonstrate that the proposed algorithms achieve reconstruction accuracy comparable to state-of-the-art TT-based geometric methods. Comments: 25 pages，。
Liping Zhang View a PDF of the paper titled Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry， 8 figures Subjects: Numerical Analysis (math.NA) ; Optimization and Control (math.OC) MSC classes: 90C30， we propose a new approach to constructing retractions compatible with the quotient structure， 15A69， 65F99 Cite as: arXiv:2606.30173 [math.NA] (or arXiv:2606.30173v1 [math.NA] for this version) https://doi.org/10.48550/arXiv.2606.30173 Focus to learn more arXiv-issued DOI via DataCite ， low-rank tensor completion within the TT-format has emerged as a prominent research focus. In this paper， our approach streamlines the horizontal projection by reducing the number of unknowns per block from a quadratic dependence on the TT-ranks to a near-half scaling， 65K05。