Block Gauss-Seidel methods for t-product tensor regression
Abstract Randomized iterative algorithms, such as the randomized Kaczmarz method and the randomized Gauss-Seidel method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights gained from studying such algorithms to develop regression methods for tensors, which are the natural setting for many application problems, e.g., image deblurring. In particular, we extend two variants of the block-randomized Gauss-Seidel method to solve a t-product tensor regression problem. We additionally develop methods for the special case where the measurement tensor is given in factorized form. We provide theoretical guarantees of the exponential convergence rate of our algorithms, accompanied by illustrative numerical simulations.
Authors
- Lara Kassab (ORCID: https://orcid.org/0000-0001-6805-4978)
- Deanna Needell (ORCID: https://orcid.org/0000-0002-8058-8638)
- Paulina Hoyos (ORCID: https://orcid.org/0009-0009-8949-998X)
- Karamatou Yacoubou Djima (ORCID: https://orcid.org/0000-0002-4888-6301)
- Jamie Haddock (ORCID: https://orcid.org/0000-0002-1449-2574)
- Alona Kryshchenko (ORCID: https://orcid.org/0000-0002-5049-0293)
- Kamila Larripa
- Alejandra Castillo
- Iryna Hartsock
- Shambhavi Suryanarayanan (ORCID: https://orcid.org/0009-0002-1424-7322)
Institutions
- Harvey Mudd College (US)
- University of California, Los Angeles (US)
- Pomona College (US)
- Wellesley College (US)
- Cal Poly Humboldt (US)
- California State University, Channel Islands (US)
- Princeton University (US)
- Moffitt Cancer Center (US)
- The University of Texas at Austin (US)
Publication Details
- Journal
- Numerical Algorithms
- Published
- 2025-10-24
- DOI
- https://doi.org/10.1007/s11075-025-02240-4
- Primary Topic
- Tensor decomposition and applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00