Toward solution of matrix equation \(X=Af(X)B+C\)

DOI10.1016/j.laa.2011.03.003zbMath1278.15021arXiv1211.0346OpenAlexW2101098094MaRDI QIDQ551297

Guang-Ren Duan, James Lam, Bin Zhou

Publication date: 15 July 2011

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

Full work available at URL: https://arxiv.org/abs/1211.0346

zbMATH Keywords

iterationclosed-form solutionsmatrix equationsnumerical solutionsStein equationsconjugated and transpose

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Iterative numerical methods for linear systems (65F10) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

On some extended block Krylov based methods for large scale nonsymmetric Stein matrix equations, Towards positive definite solutions of a class of nonlinear matrix equations, On the solution of the linear matrix equation \(X = Af(X) B + C\), Solutions to the linear transpose matrix equations and their application in control, On the Sylvester-like matrix equation \(AX+f(X)B=C\), On solutions to the matrix equations \(XB-AX=CY\) and \(XB-A\hat{X}=CY\), Parametric solutions to the discrete periodic regulator equations, On T-Sylvester equations over commutative rings, Iterative algorithms for \(X+A^{\mathrm T}X^{-1}A=I\) by using the hierarchical identification principle, Extending the CGLS algorithm for least squares solutions of the generalized Sylvester-transpose matrix equations, Computational Methods for Linear Matrix Equations, A matrix CRS iterative method for solving a class of coupled Sylvester-transpose matrix equations, The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations, Parametric Solutions to the Generalized Discrete Yakubovich-Transpose Matrix Equation, Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations, New proof of the gradient-based iterative algorithm for the Sylvester conjugate matrix equation, Biconjugate residual algorithm for solving general Sylvester-transpose matrix equations, Numerical solution of the matrix equation X — $A\bar XB$ = C in the self-adjoint case, Numerical solution of matrix equations of the Stein type in the self-adjoint case, New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation, An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations, Parametric solutions to generalized periodic Sylvester bimatrix equations, Closed-form solutions to the nonhomogeneous Yakubovich-transpose matrix equation, Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations, Adaptive parameter alternating direction algorithm for centrosymmetric solutions of a class of generalized coupled Sylvester-transpose matrix equations, A finite iterative algorithm for solving the complex generalized coupled Sylvester matrix equations by using the linear operators, A shifted complex global Lanczos method and the quasi-minimal residual variant for the Stein-conjugate matrix equation \(X + A \overline{X} B = C\), Bauer's spectral factorization method for low order multiwavelet filter design, Contour integral solutions of Sylvester-type matrix equations, On the least squares generalized Hamiltonian solution of generalized coupled Sylvester-conjugate matrix equations, New Finite Algorithm for Solving the Generalized Nonhomogeneous Yakubovich-Transpose Matrix Equation, On eigenvalues of split quaternion matrices, The Minkowski-Lyapunov equation for linear dynamics: theoretical foundations, Iterative solutions of a set of matrix equations by using the hierarchical identification principle, Positive definite solutions of the nonlinear matrix equation \(X + A^H\bar{X}^{-1}A = I\), Generalized reflexive and anti-reflexive solutions of the coupled Sylvester matrix equations via CD algorithm, Global FOM and GMRES algorithms for a class of complex matrix equations, An accelerated technique for solving one type of discrete-time algebraic Riccati equations, Modifying a numerical algorithm for solving the matrix equation X + AX T B = C, The matrix equation \(X + AX^TB = C\): Conditions for unique solvability and a numerical algorithm for its solution, Restarted global FOM and GMRES algorithms for the Stein-like matrix equation \(X + \mathcal{M}(X) = C\), Robust verification algorithm for stabilizing solutions of discrete-time algebraic Riccati equations, Numerical solution of a semilinear matrix equation of the Stein type in the normal case, Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester 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, BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix, A note on the \(\top\)-Stein matrix equation, Numerical solution of matrix equations of the form X + AX T B = C, The generalized QMRCGSTAB algorithm for solving Sylvester-transpose matrix equations, Analysis and design of complex-valued linear systems

Cites Work

• Unnamed Item
• An explicit solution to the matrix equation \(AX - XF = BY\)
• The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits
• How to solve the matrix equation \(XA-AX=f(X)\)
• Some matrix equations over a finite field
• Spectral properties of sums of certain Kronecker products
• On Smith-type iterative algorithms for the Stein matrix equation
• The general coupled matrix equations over generalized bisymmetric matrices
• Least squares solution with the minimum-norm to general matrix equations via iteration
• Explicit solution of the operator equation \(A^{*}X+X^{*}A=B\)
• Iterative algorithms for solving the matrix equation \(AXB + CX^{T}D = E\)
• On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
• ADI preconditioned Krylov methods for large Lyapunov matrix equations
• Determinant and Pfaffian of sum of skew symmetric matrices
• Positive solutions to operator equations \(AXB=C\)
• Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
• Inertia characteristics of self-adjoint matrix polynomials
• The iterative solution of the matrix equation \(XA+BX+C=0\)
• Linear matrix equations: The module theoretic approach
• Controllability, observability and the solution of AX-XB=C
• Linear operators preserving certain equivalence relations originating in system theory
• On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\)
• The matrix equation \(AXB-GXB=E\) over the quaternion field
• The solution to matrix equation \(AX+X^TC=B\)
• Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
• A Hessenberg-Schur method for the problem AX + XB= C
• Gradient based iterative algorithms for solving a class of matrix equations
• Matrix Equation $XA + BX = C$
• Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix