Iterative method to solve the generalized coupled Sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix

DOI10.1016/j.camwa.2014.04.012zbMath1362.65041OpenAlexW2022953228MaRDI QIDQ2397290

Ya-Jun Xie, Na Huang, Chang-Feng Ma

Publication date: 22 May 2017

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2014.04.012

zbMATH Keywords

iterative methodgeneralized coupled Sylvester-transpose matrix equationsleast Frobenius norm solutionsymmetric orthogonal matrixreflexive or anti-reflexive matrix

Mathematics Subject Classification ID

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

Related Items (38)

The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix ⋮ A finite iterative algorithm for the general discrete-time periodic Sylvester matrix equations ⋮ An iterative algorithm for the least Frobenius norm Hermitian and generalized skew Hamiltonian solutions of the generalized coupled Sylvester-conjugate matrix equations ⋮ Minimum-norm Hamiltonian solutions of a class of generalized Sylvester-conjugate matrix equations ⋮ The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations ⋮ Generalized conjugate direction algorithm for solving generalized coupled Sylvester transpose matrix equations over reflexive or anti-reflexive matrices ⋮ The Unified Frame of Alternating Direction Method of Multipliers for Three Classes of Matrix Equations Arising in Control Theory ⋮ New proof of the gradient-based iterative algorithm for the Sylvester conjugate matrix equation ⋮ Symmetric least squares solution of a class of Sylvester matrix equations via MINIRES algorithm ⋮ New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation ⋮ Adaptive parameter alternating direction algorithm for centrosymmetric solutions of a class of generalized coupled Sylvester-transpose matrix equations ⋮ HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations ⋮ On the least squares generalized Hamiltonian solution of generalized coupled Sylvester-conjugate matrix equations ⋮ The relaxed gradient based iterative algorithm for solving matrix equations \(A_iXB_i=F_i\) ⋮ Convergence properties of BCR method for generalized Sylvester matrix equation over generalized reflexive and anti-reflexive matrices ⋮ The BCR algorithms for solving the reflexive or anti-reflexive solutions of generalized coupled Sylvester matrix equations ⋮ Gradient-based iterative algorithms for generalized coupled Sylvester-conjugate matrix equations ⋮ Finite iterative Hermitian \(R\)-conjugate solutions of the generalized coupled Sylvester-conjugate matrix equations ⋮ Iterative Hermitian R-conjugate solutions to general coupled sylvester matrix equations ⋮ An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations ⋮ The relaxed gradient based iterative algorithm for the symmetric (skew symmetric) solution of the Sylvester equation \(A X + X B = C\) ⋮ On the convergence of conjugate direction algorithm for solving coupled Sylvester matrix equations ⋮ An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations ⋮ Two structure-preserving-doubling like algorithms for obtaining the positive definite solution to a class of nonlinear matrix equation ⋮ The scaling conjugate gradient iterative method for two types of linear matrix equations ⋮ Reduced-rank gradient-based algorithms for generalized coupled Sylvester matrix equations and its applications ⋮ The matrix iterative methods for solving a class of generalized coupled Sylvester-conjugate linear matrix equations ⋮ A modified CG algorithm for solving generalized coupled Sylvester tensor equations ⋮ Convergence of HS version of BCR algorithm to solve the generalized Sylvester matrix equation over generalized reflexive matrices ⋮ Modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations ⋮ Iterative algorithms for discrete-time periodic Sylvester matrix equations and its application in antilinear periodic system ⋮ An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations ⋮ AN ITERATIVE ALGORITHM FOR SOLVING A CLASS OF GENERALIZED COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS OVER BISYMMETRIC OR SKEW-ANTI-SYMMETRIC MATRICES ⋮ BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix ⋮ Computing symmetric solutions of general Sylvester matrix equations via Lanczos version of biconjugate residual algorithm ⋮ Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations ⋮ Conjugate gradient-based iterative algorithm for solving generalized periodic coupled Sylvester matrix equations ⋮ On a transformation of the ∗-congruence Sylvester equation for the least squares optimization

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