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Journal Articles Linear and Multilinear Algebra Year : 2022

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

Fatemeh Panjeh Ali Beik
Mehdi Najafi-Kalyani

Abstract

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 M-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.
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hal-04413479 , version 1 (23-01-2024)

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Fatemeh Panjeh Ali Beik, Mehdi Najafi-Kalyani, Khalide Jbilou. Preconditioned iterative methods for multi-linear systems based on the majorization matrix. Linear and Multilinear Algebra, 2022, 70 (20), pp.5827-5846. ⟨10.1080/03081087.2021.1931654⟩. ⟨hal-04413479⟩
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