Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish concise notation that is suitable for the analysis and development of block tensor algorithms, prove several useful block tensor identities, and make precise the notion of a block tensor unfolding.
Effective algorithms for tensor train decomposition via the UTV framework
School of Mathematical Sciences, Chengdu University of Technology（成都理工大学数学科学学院）；School of Mathematics and Statistics, Guizhou University（贵州大学数学与统计学院）；School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University（复旦大学数学科学系与非线性科学数学重点实验室）
A Tensor Greedy Double-Block Extended Kaczmarz Method for Inconsistent Tensor Linear Systems under the t-product
African Institute of Mathematical Sciences（非洲数学科学学院）；African Master’s of Machine Intelligence（非洲机器学习硕士项目）；Institute for Analysis and Algebra, TU Braunschweig（不伦瑞克工业大学分析与代数研究所）
Randomized block Krylov method for approximation of truncated tensor SVD
Research Center of the Artificial Intelligence Institute, and Lab of Machine Learning and Knowledge Representation, Innopolis University（因诺波利斯大学人工智能研究所研究中心及机器学习和知识表示实验室）；Department of Teleinformatics Engineering, Federal University of Ceara（福塔莱萨塞阿拉联邦大学电信信息工程系）
A Novel Block-Alternating Iterative Algorithm for Retrieving Top-$k$ Elements from Factorized Tensors
the School of Mathematics and Computational Science, Xiangtan University（湘潭大学数学与计算科学学院）；the Department of Broadband Communications, Pengcheng Laboratory（鹏城实验室宽带通信研究所）
Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor
School of Mathematics, University of Minnesota（明尼苏达大学数学学院）；Oden Institute for Computational Engineering and Sciences, University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学学院）
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Computation of extreme eigenvalues in higher dimensions using block tensor train format
Max-Planck Institute for Mathematics in the Sciences（马克斯·普朗克科学促进会数学与科学研究所）；Institute of Numerical Mathematics of Russian Academy of Sciences（俄罗斯科学院计算数学研究所）；University of Southampton（南安普顿大学）
