Preconditioned iterative methods for multi-linear systems based on the majorization matrix

This paper mainly deals with applying a general class of preconditioners to accelerate the convergence speed of some iterative schemes for solving multi-linear systems whose coefficient tensors are strong -tensors. Theoretical results are established to analyse the performance of a general class of...

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Bibliographic Details
Published in:Linear & multilinear algebra 2022-12, Vol.70 (20), p.5827-5846
Main Authors: Beik, Fatemeh Panjeh Ali, Najafi-Kalyani, Mehdi, Jbilou, Khalide
Format: Article
Language:English
Subjects:
convergence
Iterative method
Iterative methods
Linear systems
Mathematical analysis
Mathematics
multi-linear system
preconditioner
Subspace methods
tensor
Tensors
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Summary:This paper mainly deals with applying a general class of preconditioners to accelerate the convergence speed of some iterative schemes for solving multi-linear systems whose coefficient tensors are strong -tensors. Theoretical results are established to analyse the performance of a general class of preconditioners extracted from the majorization matrix associated with the coefficient tensor. Brief discussions are included in using a Krylov subspace method based on the Hessenberg process to solve the mentioned problem. For the sake of generality, we consider multi-linear systems with multiple right-hand sides. Numerical experiments are reported to illustrate the validity of the presented theoretical results.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2021.1931654