2024/09/13 by Krushnachandra Panigrahy, Biswarup Karmakar, Panigrahy, Krushnachandra +7
Computer Science · Mathematics · #Computational Physics and Python Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2409.08743
openalex publication_date 2024/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra, and the choice of tensor product determines the algorithms that can be directly applied. This study introduced a novel full-rank decomposition and M-\mcQDR decomposition for third-order tensors based on M-product. Then, we designed algorithms for computing these two decompositions along with the Moore-Penrose inverse, and outer inverse of the tensors. In support of these theoretical results, a few numerical examples were discussed. In addition, we derive exact expressions for the outer inverses of tensors using symbolic tensor (tensors with polynomial entries) computation. We designed efficient algorithms to compute the Moore-Penrose inverse of symbolic tensors. The prowess of the proposed M-\mcQDR decomposition for third-order tensors is applied to compress lossy color images.