Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices
From MaRDI portal
Publication:5965416
DOI10.1016/j.laa.2016.02.013zbMath1332.15006OpenAlexW2280628847MaRDI QIDQ5965416
Oscar Mauricio Agudelo, Zhuo-Heng He, Qing-Wen Wang, Bart De Moor
Publication date: 3 March 2016
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2016.02.013
Factorization of matrices (15A23) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03) Canonical forms, reductions, classification (15A21)
Related Items
On the Hermitian and skew-Hermitian splitting-like iteration approach for solving complex continuous-time algebraic Riccati matrix equation ⋮ A simple method for solving matrix equations \(AXB = D\) and \(GXH = C\) ⋮ Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E ⋮ A note on the solvability for generalized Sylvester equations ⋮ On the general solutions to some systems of quaternion matrix equations ⋮ A system of coupled two-sided Sylvester-type tensor equations over the quaternion algebra ⋮ A system of Sylvester-type quaternion matrix equations with ten variables ⋮ Least-squares solutions of generalized Sylvester-type quaternion matrix equations ⋮ Unnamed Item ⋮ A coupled quaternion matrix equations with applications ⋮ A system of coupled quaternion matrix equations with seven unknowns and its applications ⋮ Cramer's rules of \(\eta \)-(skew-)Hermitian solutions to the quaternion Sylvester-type matrix equations ⋮ The general solution to a system of linear coupled quaternion matrix equations with an application ⋮ Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation ⋮ The relaxed gradient based iterative algorithm for solving matrix equations \(A_iXB_i=F_i\) ⋮ Factorization of Generalized Theta Functions Revisited ⋮ A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations ⋮ A simultaneous decomposition for seven matrices with applications ⋮ Structure, properties and applications of some simultaneous decompositions for quaternion matrices involving \(\phi\)-skew-Hermicity ⋮ Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations ⋮ Simultaneous decomposition of quaternion matrices involving \(\eta\)-Hermicity with applications ⋮ Constrained two-sided coupled Sylvester-type quaternion matrix equations ⋮ Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore-Penrose inverse ⋮ The complete equivalence canonical form of four matrices over an arbitrary division ring ⋮ A system of quaternary coupled Sylvester-type real quaternion matrix equations ⋮ Cramer's rules for Sylvester quaternion matrix equation and its special cases ⋮ Some applications of a decomposition for five quaternion matrices in control system and color image processing ⋮ Unnamed Item ⋮ The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations ⋮ The least square solution with the least norm to a system of quaternion matrix equations ⋮ Finite iterative solutions to periodic Sylvester matrix equations ⋮ Solutions to linear bimatrix equations with applications to pole assignment of complex-valued linear systems ⋮ A Numerical Approach To Generalized Periodic Sylvester Matrix Equation ⋮ On Hermitian solutions of the reduced biquaternion matrix equation (AXB,CXD) = (E,G) ⋮ Pure PSVD approach to Sylvester-type quaternion matrix equations ⋮ Decomposition for a quaternion tensor triplet with applications ⋮ The double-step scale splitting method for solving complex Sylvester matrix equation ⋮ The general solution to a system of coupled Sylvester-type quaternion tensor equations involving \(\eta\)-Hermicity ⋮ Determinantal representations of solutions to systems of two-sided quaternion matrix equations ⋮ Some new results on a system of Sylvester-type quaternion matrix equations ⋮ A System of Matrix Equations over the Quaternion Algebra with Applications
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Simultaneous solutions of matrix equations and simultaneous equivalence of matrices
- Systems of coupled generalized Sylvester matrix equations
- An efficient algorithm for the solution of a coupled Sylvester equation appearing in descriptor systems
- Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
- A tree of generalizations of the ordinary singular value decomposition
- On Smith-type iterative algorithms for the Stein matrix equation
- Almost non-interacting control by measurement feedback
- The matrix equation \(X-AXB=C\) and an analogue of Roth's theorem
- The matrix equation AXB+CYD=E
- The matrix equation \(AX-YB=C\)
- On the finite transmission zero assignment problem
- On solutions of matrix equation \(AXB+CYD=F\)
- A QR-type reduction for computing the SVD of a general matrix product/quotient
- Sylvester equations and projection-based model reduction.
- On a variational formulation of the QSVD and the RSVD
- Coupled and constrained Sylvester equations in system design
- A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
- The solution of the equation \(AX + X^{\star}B =0\)
- Solving SDGE models: a new algorithm for the Sylvester equation
- Solvability conditions and general solution for mixed Sylvester equations
- A common solution to a pair of linear matrix equations over a principal ideal domain
- On the Computation of the Restricted Singular Value Decomposition via the Cosine-Sine Decomposition
- Robust fault detection using Luenberger-type unknown input observers-a parametric approach
- The Restricted Singular Value Decomposition of Matrix Triplets
- Inertia and Rank Characterizations of Some Matrix Expressions
- Robust and well-conditioned eigenstructure assignment via sylvester's equation
- Computing the Singular Value Decomposition of a Product of Two Matrices
- Eigenvalue-generalized eigenvector assignment by output feedback
- Methods for the solution ofAXD−BXC=E and its application in the numerical solution of implicit ordinary differential equations
- Towards a Generalized Singular Value Decomposition
- The Restricted Singular Value Decomposition: Properties and Applications
- The Equation $AXB + CYD = E$ over a Principal Ideal Domain
- Generalizations of the Singular Value and QR-Decompositions
- Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
- Generalizing the Singular Value Decomposition
- Generalized Schur methods with condition estimators for solving the generalized Sylvester equation
- Minimal rank completions of partial banded matrices
- Output feedback eigenstructure assignment using two Sylvester equations
- On the Structure of Generalized Singular Value and QR Decompositions
- An eigenstructure assignment algorithm for the design of fault detection filters
- Consistency of a pair of generalized Sylvester equations
- On a Variational Formulation of the Generalized Singular Value Decomposition
- Application of ADI Iterative Methods to the Restoration of Noisy Images
- Design of unknown input observers and robust fault detection filters
- Coupled Sylvester-type Matrix Equations and Block Diagonalization
- Recursive blocked algorithms for solving triangular systems—Part I
- Recursive blocked algorithms for solving triangular systems—Part II
- Best Approximate Solution of Matrix Equation AXB+CYD=E
- A Pair of Mixed Generalized Sylvester Matrix Equations
- Approximation of Large-Scale Dynamical Systems
- The Equations AX - YB = C and AX - XB = C in Matrices