An efficient algorithm for solving general coupled matrix equations and its application
From MaRDI portal
Publication:604125
DOI10.1016/j.mcm.2009.12.022zbMath1208.65054OpenAlexW2043218140MaRDI QIDQ604125
Mehdi Dehghan, Masoud Hajarian
Publication date: 8 November 2010
Published in: Mathematical and Computer Modelling (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.mcm.2009.12.022
iterative algorithmnumerical examplesconjugate gradient methodJacobi methodGauss-Seidel methodsSylvester matrix equationgeneral coupled matrix equationsLyapunov matrix equations\((R,S)\)-skew symmetric matrices\((R,S)\)-symmetric matricesleast Frobenius norm solution groupoptimal approximation solution group
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Cites Work
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- An explicit solution to the matrix equation \(AX - XF = BY\)
- Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation \(A_1X_1B_1+A_2X_2B_2=C\)
- The general coupled matrix equations over generalized bisymmetric matrices
- A lower bound for the product of eigenvalues of solutions to matrix equations
- An efficient algorithm for the least-squares reflexive solution of the matrix equation \(A_{1}XB_{1} = C_{1}, A_{2}XB_{2} = C_{2}\)
- 2-norm based recursive design of transmultiplexers with designable filter length
- A new projection method for solving large Sylvester equations
- An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
- Minimal residual methods augmented with eigenvectors for solving Sylvester equations and generalized Sylvester equations
- An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices
- The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations
- Weighted least squares solutions to general coupled Sylvester matrix equations
- Ranks and the least-norm of the general solution to a system of quaternion matrix equations
- Gradient based iterative algorithm for solving coupled matrix equations
- Solutions to a family of matrix equations by using the Kronecker matrix polynomials
- A system of real quaternion matrix equations with applications
- Iterative solution of the Lyapunov matrix equation
- SOR for \(AX-XB=C\)
- Hierarchical gradient-based identification of multivariable discrete-time systems
- An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation \(AXB\)=\(C\)
- A modified low-rank Smith method for large-scale Lyapunov equations
- Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices
- Least-squares solution of \(F=PG\) over positive semidefinite symmetric \(P\)
- Perturbation theory and backward error for \(AX - XB = C\)
- The polynomial solution to the Sylvester matrix equation
- An iterative algorithm for solving a pair of matrix equations \(AYB=E\), \(CYD=F\) over generalized centro-symmetric matrices
- The common solution to six quaternion matrix equations with applications
- On the generalized Sylvester mapping and matrix equations
- Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
- Use of near-breakdowns in the block Arnoldi method for solving large Sylvester equations
- Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
- The general solution to a system of real quaternion matrix equations
- Iterative least-squares solutions of coupled sylvester matrix equations
- A new solution to the generalized Sylvester matrix equation \(AV-EVF=BW\)
- Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
- On Iterative Solutions of General Coupled Matrix Equations
- A new solvable condition for a pair of generalized Sylvester equations
- Kalman filter‐based adaptive control for networked systems with unknown parameters and randomly missing outputs
- On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations
- An efficient iterative method for solving the matrix equationAXB +CYD =E
- ON THE REFLEXIVE SOLUTIONS OF THE MATRIX EQUATION AXB + CYD = E
- A Riccati Transformation Method for Solving Linear BVP<scp>s</scp>. I: Theoretical Aspects
- Methods for the solution ofAXD−BXC=E and its application in the numerical solution of implicit ordinary differential equations
- Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
- Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
- Generalized Schur methods with condition estimators for solving the generalized Sylvester equation
- LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs
- Generalized Reflexive Matrices: Special Properties and Applications
- A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
- Application of ADI Iterative Methods to the Restoration of Noisy Images
- Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains
- Hierarchical least squares identification methods for multivariable systems
- Gradient based iterative algorithms for solving a class of matrix equations
- Characterization and Properties of (R,S)-Symmetric, (R,S)-Skew Symmetric, and (R,S)-Conjugate Matrices
- Solutions to generalized Sylvester matrix equation by Schur decomposition
- Matrix Equation $XA + BX = C$
- The Use of Conjugate Gradients for Systems of Linear Equations Possessing “Property A”
- Block Krylov subspace methods for solving large Sylvester equations
