Preconditioned tensor splitting AOR iterative methods for H‐tensor equations

Summary Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) M‐tensors. In this article, we introduce H‐splitting and H‐compatible splitting and investigate the relationship between these different...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2020-12, Vol.27 (6), p.n/a
Main Authors: Wang, Xuezhong, Che, Maolin, Wei, Yimin
Format: Article
Language:English
Subjects:
Convergence
H‐splitting
Iterative methods
Mathematical analysis
preconditioned AOR method
Splitting
tensor equations
Tensors
H‐tensors
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Summary:Summary Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) M‐tensors. In this article, we introduce H‐splitting and H‐compatible splitting and investigate the relationship between these different splittings and their convergence. Meanwhile, we also consider a preconditioned AOR iterative method for solving tensor equations with nonsingular H‐tensors. We prove its convergence and give a comparison result on the spectral radius of the iteration tensor for the case when A is a nonsingular M‐tensor. Numerical examples are also given to illustrate our methods.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2329