Extending BiCG and BiCR methods to solve the Stein tensor equation

DOI10.1016/j.camwa.2019.01.024zbMath1442.65068OpenAlexW2911992324WikidataQ128368403 ScholiaQ128368403MaRDI QIDQ2204031

Xiangjian Xu, Qing-Wen Wang

Publication date: 2 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2019.01.024

zbMATH Keywords

iterative algorithm\(k\)-mode productbiconjugate gradients (BiCG) methodbiconjugate residual (BiCR) methodStein tensor equation

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Multilinear algebra, tensor calculus (15A69) Numerical methods for matrix equations (65F45)

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Uses Software

• TensorToolbox

Cites Work

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• Tensor Decompositions and Applications
• Extending the CGLS algorithm for least squares solutions of the generalized Sylvester-transpose matrix equations
• On solving the Lyapunov and Stein equations for a companion matrix
• On Smith-type iterative algorithms for the Stein matrix equation
• Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method
• On the Lyapunov and Stein equations
• A functional approach to the Stein equation
• On the Lyapunov and Stein equations. II.
• Iterative and direct Chebyshev collocation spectral methods for one-dimensional radiative heat transfer
• An extension of the conjugate residual method to nonsymmetric linear systems
• SOR for \(AX-XB=C\)
• Perturbation theory for matrix equations
• Possible inertia combinations in the Stein and Lyapunov equations
• A projection method and Kronecker product preconditioner for solving Sylvester tensor equations
• Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations
• Symmetric least squares solution of a class of Sylvester matrix equations via MINIRES algorithm
• On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations
• Backward error and perturbation bounds for high order Sylvester tensor equation
• Krylov Subspace Methods for Linear Systems with Tensor Product Structure
• Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
• A Kronecker product approximate preconditioner for SANs
• Efficient MATLAB Computations with Sparse and Factored Tensors
• A Hessenberg-Schur method for the problem AX + XB= C
• The Alternating Direction Methods for Solving the Sylvester-Type Matrix Equation<br> <em>AXb + CX^⊤D = E^*</em>
• Tensor Analysis
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]

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