Preconditioned Jacobi type method for solving multi-linear systems with \(\mathcal{M}\)-tensors

DOI10.1016/j.aml.2020.106287zbMath1439.65038OpenAlexW3006091091WikidataQ114210606 ScholiaQ114210606MaRDI QIDQ2176509

Zhen Chen, Yaxiu Zhang, Qilong Liu

Publication date: 4 May 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106287

zbMATH Keywords

multi-linear systemstensor splittingpreconditioned Jacobi type methodsstrong \(\mathcal{M}\)-tensors

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items

A fast sketching-based algorithm for rank-\((L,L,1)\) block term decomposition ⋮ Existence and uniqueness of positive solution for multilinear systems with generalized strong \(\mathcal{M}\)-tensor ⋮ PRECONDITIONED AOR ITERATIVE METHODS FOR SOLVING MULTI-LINEAR SYSTEMS WITH 𝓜-TENSOR ⋮ Iterative refinement method by higher-order singular value decomposition for solving multi-linear systems ⋮ A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with \(\mathcal{M}\)-tensors ⋮ Slice tensor splitting method for solving tensor equation ⋮ A new preconditioner for Gauss-Seidel method for solving multi-linear systems ⋮ A new preconditioned AOR-type method for \(\mathcal{M}\)-tensor equation ⋮ A general preconditioner for tensor complementarity problems ⋮ Unnamed Item ⋮ A general preconditioner accelerated SOR-type iterative method for multi-linear systems with \(\mathcal{Z}\)-tensors ⋮ Fast verified computation for positive solutions to \(\mathcal{M} \)-tensor multi-linear systems and Perron vectors of a kind of weakly irreducible nonnegative tensors ⋮ Preconditioned iterative methods for multi-linear systems based on the majorization matrix

Cites Work

• Unnamed Item
• Alternating projection method for a class of tensor equations
• Comparison results for splitting iterations for solving multi-linear systems
• The tensor splitting with application to solve multi-linear systems
• A Levenberg-Marquardt method for solving semi-symmetric tensor equations
• Tensor methods for solving symmetric \({\mathcal {M}}\)-tensor systems
• On the uniqueness of the positive Z-eigenvector for nonnegative tensors
• A globally and quadratically convergent algorithm for solving multilinear systems with \(\mathcal {M}\)-tensors
• Tensor absolute value equations
• Preconditioned tensor splitting iterations method for solving multi-linear systems
• Generalized tensor equations with leading structured tensors
• Neural network approach for solving nonsingular multi-linear tensor systems
• An equivalent tensor equation to the tensor complementarity problem with positive semi-definite \(Z\)-tensor
• Solving multi-linear systems with \(\mathcal {M}\)-tensors
• A homotopy method for solving multilinear systems with M-tensors
• \(M\)-tensors and nonsingular \(M\)-tensors
• An eigenvalue problem for even order tensors with its applications
• $M$-Tensors and Some Applications
• Splitting methods for tensor equations
• On the inverse of a tensor