Comparison results for splitting iterations for solving multi-linear systems
type: Item
instance of: scholarly article
title: Comparison results for splitting iterations for solving multi-linear systems
zbMATH Open document ID: 1432.65037
author: Wen Li
author: Dongdong Liu
author: Seak-Weng Vong
published in: Applied Numerical Mathematics
publication date: 2018-09-07T00:00:00Z
review text: It is known that the spectral radius of the iterative tensor associated with a stationary splitting method (like the Jacobi or Gauss-Seidel methods) can be seen as an approximate convergence rate for solving multi-linear systems. The paper first gives some spectral radius comparisons between different types of tensor splittings. Then, it proposes a particular preconditioned tensor splitting method with a tensor analogue of a bidiagonal preconditioner. The corresponding spectral radius is analyzed in dependence of the chosen entries of this preconditioner and compared with the situation without preconditioner. Numerical examples are given to demonstrate the efficiency of the preconditioned methods applied in both a Gauss-Seidel and an SOR-type of setting.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6933820
zbMATH Keywords: tensor splitting
zbMATH Keywords: tensor spectral radius
zbMATH Keywords: multi-linear systems
zbMATH Keywords: tensor preconditioning
zbMATH Keywords: stationary iterative methods
MaRDI profile type: Publication
full work available at URL: j.apnum.2018.07.009
OpenAlex ID: W2883260191
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Wikidata QID: Q129474573
DOI: 10.1016/J.APNUM.2018.07.009
description: scientific article; zbMATH DE number 6933820