The relaxed gradient based iterative algorithm for solving matrix equations \(A_iXB_i=F_i\)

DOI10.1016/j.camwa.2017.05.008zbMath1382.65093OpenAlexW2620489511MaRDI QIDQ1704197

Xingping Sheng, Sun, Weiwei

Publication date: 9 March 2018

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.05.008

zbMATH Keywords

numerical solutionmatrix equationsrelaxation factorrelaxed gradient based iterative algorithm

Mathematics Subject Classification ID

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

Related Items (7)

Delayed over-relaxation in iterative schemes to solve rank deficient linear system of (matrix) equations ⋮ Iterative solution to a class of complex matrix equations and its application in time-varying linear system ⋮ Cyclic gradient based iterative algorithm for a class of generalized coupled Sylvester-conjugate matrix equations ⋮ Fast linear inversion for highly overdetermined inverse scattering problems ⋮ An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations ⋮ The steepest descent of gradient-based iterative method for solving rectangular linear systems with an application to Poisson's equation ⋮ Conjugate gradient-based iterative algorithm for solving generalized periodic coupled Sylvester matrix equations

Cites Work

• A modified gradient based algorithm for solving Sylvester equations
• Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation \(AX=B\)
• The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation
• Iterative solutions to matrix equations of the form \(A_{i}XB_{i}=F_{i}\)
• Least-squares solution with the minimum-norm for the matrix equation \((A\times B,G\times H) = (C,D)\)
• Ranks of least squares solutions of the matrix equation \(AXB=C\)
• Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions
• An iterative algorithm for the least squares bisymmetric solutions of the matrix equations \(A_{1}XB_{1}=C_{1},A_{2}XB_{2}=C_{2}\)
• Successive projection iterative method for solving matrix equation \(AX=B\)
• The residual based extended least squares identification method for dual-rate systems
• Gradient based iterative algorithm for solving coupled matrix equations
• On the reducibility of centrosymmetric matices - applications in engineering problems
• On the generalized reflexive and anti-reflexive solutions to a system of matrix equations
• Hierarchical gradient-based identification of multivariable discrete-time systems
• Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices
• The scaling conjugate gradient iterative method for two types of linear matrix equations
• Iterative methods to solve the generalized coupled Sylvester-conjugate matrix equations for obtaining the centrally symmetric (centrally antisymmetric) matrix solutions
• A finite iterative method for solving a pair of linear matrix equations \((AXB,CXD)=(E,F)\)
• Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems
• An iterative algorithm for solving a pair of matrix equations \(AYB=E\), \(CYD=F\) over generalized centro-symmetric matrices
• Iterative method to solve the generalized coupled Sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix
• The modified accelerated Bregman method for regularized basis pursuit problem
• Least squares solutions to \(AX = B\) for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation
• Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
• The block least squares method for solving nonsymmetric linear systems with multiple right-hand sides
• Global least squares method (Gl-LSQR) for solving general linear systems with several right-hand sides
• Eigenvectors of certain matrices
• The Solutions of Matrix Equation $AX=B$ Over a Matrix Inequality Constraint
• The consistency and the exact solutions to a system of matrix equations
• A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations
• The general solutions to some systems of matrix equations
• Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations
• Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors
• Hierarchical identification of lifted state-space models for general dual-rate systems
• The structure of weighting coefficient matrices of harmonic differential quadrature and its applications
• Hierarchical least squares identification methods for multivariable systems
• Gradient based iterative algorithms for solving a class of matrix equations
• The Inverse Eigenproblem of Centrosymmetric Matrices with a Submatrix Constraint and Its Approximation
• Gradient-based maximal convergence rate iterative method for solving linear matrix equations
• Observer-based Adaptive fuzzy control of time-delay uncertain nonlinear systems
• A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications
• Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices

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