Comparison results for splitting iterations for solving multi-linear systems

DOI10.1016/j.apnum.2018.07.009zbMath1432.65037OpenAlexW2883260191WikidataQ129474573 ScholiaQ129474573MaRDI QIDQ1671737

Dongdong Liu, Wen Li, Seak Weng Vong

Publication date: 7 September 2018

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.07.009

zbMATH Keywords

stationary iterative methodsmulti-linear systemstensor preconditioningtensor spectral radiustensor splitting

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Multilinear algebra, tensor calculus (15A69) Preconditioners for iterative methods (65F08)

Related Items (24)

Solving tensor absolute value equation ⋮ Novel accelerated methods of tensor splitting iteration for solving multi-systems ⋮ Preconditioned Jacobi type method for solving multi-linear systems with \(\mathcal{M}\)-tensors ⋮ A new preconditioned SOR method for solving multi-linear systems with an \(\mathcal{M} \)-tensor ⋮ Accelerated dynamical approaches for finding the unique positive solution of \(\mathcal{KS}\)-tensor equations ⋮ PRECONDITIONED AOR ITERATIVE METHODS FOR SOLVING MULTI-LINEAR SYSTEMS WITH 𝓜-TENSOR ⋮ A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with \(\mathcal{M}\)-tensors ⋮ The tensor splitting methods for solving tensor absolute value equation ⋮ 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 ⋮ Richardson Iterative Method for Solving Multi-Linear System with M-Tensor ⋮ A general preconditioner for tensor complementarity problems ⋮ Interval tensors and their application in solving multi-linear systems of equations ⋮ Unnamed Item ⋮ Preconditioned tensor splitting iterations method for solving multi-linear systems ⋮ A nonnegativity preserving algorithm for multilinear systems with nonsingular \(\mathcal{M}\)-tensors ⋮ Neural network approach for solving nonsingular multi-linear tensor systems ⋮ A homotopy method for solving multilinear systems with strong completely positive tensors ⋮ 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 ⋮ On the solvability of tensor absolute value equations ⋮ A preconditioned tensor splitting iteration method and associated global correction technique for solving multilinear systems ⋮ Preconditioned iterative methods for multi-linear systems based on the majorization matrix

Cites Work

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• Tensor Decompositions and Applications
• Modified iterative methods for consistent linear systems
• Perron-Frobenius theorem for nonnegative tensors
• Improving Jacobi and Gauss-Seidel iterations
• Improving the modified Gauss-Seidel method for \(Z\)-matrices
• Modified Gauss-Seidel type methods and Jacobi type methods for Z-matrices
• The tensor splitting with application to solve multi-linear systems
• Tensor methods for solving symmetric \({\mathcal {M}}\)-tensor systems
• More on modifications and improvements of classical iterative schemes for \(M\)-matrices
• Solving multi-linear systems with \(\mathcal {M}\)-tensors
• \(M\)-tensors and nonsingular \(M\)-tensors
• Eigenvalues of a real supersymmetric tensor
• $M$-Tensors and Some Applications
• Further Results for Perron–Frobenius Theorem for Nonnegative Tensors
• Splitting methods for tensor equations
• Tensor Analysis
• Matrix Iterative Analysis
• On the inverse of a tensor

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