The (R, S)-symmetric least squares solutions of the general coupled matrix equations

DOI10.1080/03081087.2014.918615zbMath1319.65031OpenAlexW2087494851MaRDI QIDQ5175381

Zhuo-Hua Peng

Publication date: 20 February 2015

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

Full work available at URL: https://doi.org/10.1080/03081087.2014.918615

zbMATH Keywords

algorithmnumerical exampleiterative methodleast squares solutiongeneral coupled matrix equations\((R,S)\)-symmetric matrixleast norm solution

Mathematics Subject Classification ID

Related Items (7)

Convergence Results of the Biconjugate Residual Algorithm for Solving Generalized Sylvester Matrix Equation ⋮ Generalized conjugate direction algorithm for solving the general coupled matrix equations over symmetric matrices ⋮ Generalized reflexive and anti-reflexive solutions of the coupled Sylvester matrix equations via CD algorithm ⋮ Iterative algorithms for least-squares solutions of a quaternion matrix equation ⋮ An iterative algorithm for solving the generalized Sylvester-conjugate matrix equation ⋮ GRADIENT BASED ITERATIVE ALGORITHM TO SOLVE GENERAL COUPLED DISCRETE-TIME PERIODIC MATRIX EQUATIONS OVER GENERALIZED REFLEXIVE MATRICES ⋮ Modified CGLS iterative algorithm for solving the generalized Sylvester-conjugate matrix equation

Cites Work

• Gradient based and least squares based iterative algorithms for matrix equations \(AXB + CX^{T}D = F\)
• Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
• Iterative solutions to matrix equations of the form \(A_{i}XB_{i}=F_{i}\)
• Ranks and the least-norm of the general solution to a system of quaternion matrix equations
• Singular value and generalized singular value decompositions and the solution of linear matrix equations
• The symmetric solution of the matrix equations \(AX+YA=C, AXA^ t+BYB^ t=C\), and \((A^ tXA, B^ tXB)=(C,D)\)
• Least squares solution of the quaternion matrix equation with the least norm
• On Iterative Solutions of General Coupled Matrix Equations

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