2020/04/12 by Fatemeh Panjeh Ali Beik, F. P. A. Beik, Alaa El Ichi +8 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #15A69 #15A72 #65B05 #65F22 #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Tensor decomposition and applications #cs.NA #math.NA #msc:15A69 #msc:15A72 #msc:65B05 #msc:65F22
paper · pdf · doi:10.48550/arxiv.2004.05630
This is a research paper
arxiv created 2020/04/12 · openalex publication_date 2020/04/12 · arxiv updated 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly develop the well-known vector and matrix polynomial extrapolation methods in tensor framework. To this end, some new products between tensors are defined and the concept of positive definitiveness is extended for tensors corresponding to T-product. Furthermore, we discuss on the solution of least-squares problem associated with a tensor equation using Tensor Singular Value Decomposition (TSVD). Motivated by the effectiveness of proposed vector extrapolation method in [Numer. Algorithms, 51 (2009), 195--208], we describe how an extrapolation technique can be also implemented on the sequence of tensors produced by truncated TSVD (TTSVD) for solving possibly ill-posed tensor equations.