TL;DR
This paper proposes a randomized tensor QLP decomposition (rt-QLP) for third-order tensors without pivoting, extending the matrix-based QLP to the tensor setting in the transformed domain.
This work develops TTD- and HTD-based formulations for the T-product and its associated key algebra by operating directly on the factor matrices or tensors of the decompositions of the decompositions.
Two randomized algorithms within the sketched GMRES framework that replace full Arnoldi orthogonalization with short recurrences are proposed, providing robustness across a wide range of problems and outperform standard low-rank Tucker solvers in symmetric and non-symmetric settings.
A finite-step approximation guarantee that approaches the classical $1-1/e$ factor as direction certification becomes exact and finite-step residual error vanishes is established.
A novel semi-tensor product for third-order tensors under the t-product framework induced by arbitrary invertible linear transforms is introduced, yielding an accelerated multi-term randomized semi-tensor product SVD algorithm that achieves a balance between reconstruction accuracy and computational efficiency.
A structure-regularized CP (SR-CP) framework that uses a unified quadratic penalty to encode diverse structural priors through positive semidefinite matrices and a soft orthogonality-promoting penalty is further introduced to enhance component distinctiveness and numerical stability.
Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise ev...
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