Restarted Nonnegativity Preserving Tensor Splitting Methods via Relaxed Anderson Acceleration for Solving Multi-linear Systems

2022/11/20 by Dongdong Liu, Liu, Dongdong Liu Ting Hua nd Xifu
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2211.10857

openalex publication_date 2022/11/20 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28

Abstract

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves nonnegativity for every iterative step and improves the existing ones. Furthermore, the convergence analysis of the proposed method is given. The new algorithm performs effectively for numerical experiments.

Related

• A tensor Alternating Anderson-Richardson method for solving multilinear systems with M-tensors
• A Splitting Augmented Lagrangian Method for Low Multilinear-Rank Tensor Recovery
• A nonnegativity preserving algorithm for multilinear systems with nonsingular M-tensors
• Fast and flexible preconditioners for solving multilinear systems
• Nesterov Acceleration of Alternating Least Squares for Canonical Tensor Decomposition: Momentum Step Size Selection and Restart Mechanisms