A shift-splitting hierarchical identification method for solving Lyapunov matrix equations

DOI10.1016/j.laa.2008.01.010zbMath1169.65037OpenAlexW2082799093MaRDI QIDQ1002254

Huiyan Xue, Chuanqing Gu

Publication date: 25 February 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.01.010

zbMATH Keywords

algorithmconvergencenumerical examplesiterative methodmatrix equationshierarchical identification principleLyapunov matrix equationsshift-splittingSylvester matrix equations

Mathematics Subject Classification ID

Related Items (16)

Extending the CGLS algorithm for least squares solutions of the generalized Sylvester-transpose matrix equations ⋮ Least squares solution of the linear operator equation ⋮ Shift-Splitting Iteration Method and Its Variants for Solving Continuous Sylvester Equations ⋮ A matrix CRS iterative method for solving a class of coupled Sylvester-transpose matrix equations ⋮ On modified HSS iteration methods for continuous Sylvester equations ⋮ New proof of the gradient-based iterative algorithm for the Sylvester conjugate matrix equation ⋮ On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations ⋮ New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation ⋮ Iterative solutions to coupled Sylvester-transpose matrix equations ⋮ A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations ⋮ Preconditioned HSS iteration method and its non-alternating variant for continuous Sylvester equations ⋮ On the NPHSS-KPIK iteration method for low-rank complex Sylvester equations arising from time-periodic fractional diffusion equations ⋮ An accelerated Jacobi-gradient based iterative algorithm for solving sylvester matrix equations ⋮ LSQR iterative common symmetric solutions to matrix equations \(AXB = E\) and \(CXD = F\) ⋮ Numerical algorithms for solving discrete Lyapunov tensor equation ⋮ On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations

Cites Work

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• A modified low-rank Smith method for large-scale Lyapunov equations
• Iterative least-squares solutions of coupled sylvester matrix equations
• On Iterative Solutions of General Coupled Matrix Equations
• A Hessenberg-Schur method for the problem AX + XB= C
• Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yakubovich equations
• A numerical algorithm to solve<tex>A^{T}XA - X = Q</tex>
• On the solution of the discrete-time Lyapunov matrix equation in controllable canonical form
• Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Hierarchical least squares identification methods for multivariable systems
• Gradient based iterative algorithms for solving a class of matrix equations
• A technique for solving the extended discrete Lyapunov matrix equation

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