Randomized algorithms for the approximations of Tucker and the tensor train decompositions

• Published in: Advances in computational mathematics Vol. 45; no. 1; pp. 395 - 428
• Main Authors: Che, Maolin, Wei, Yimin
• Format: Journal Article
• Language: English
• Published: New York Springer US 05.02.2019; Springer Nature B.V
• Subjects: Adaptive algorithms; Algorithms; Computation; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Decomposition; Error analysis; Mathematical analysis; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Randomization; Robustness (mathematics); Software; Tensors; Visualization; Kronecker structures; Multilinear rank; TT-approximation; TT-rank; 15A69; Adaptive randomized algorithms; Tensor train decomposition; 15A18; 65F10; Low multilinear rank approximation; Randomized algorithms; 65F15; Tucker decomposition

Randomized algorithms provide a powerful tool for scientific computing. Compared with standard deterministic algorithms, randomized algorithms are often faster and robust. The main purpose of this paper is to design adaptive randomized algorithms for computing the approximate tensor decompositions....