Least-squares solution with the minimum-norm for the matrix equation \(A^T XB + B^T X^T A = D\) and its applications

DOI10.1007/s10255-007-0369-0zbMath1177.15018OpenAlexW2033498088MaRDI QIDQ1036873

Yuan Lei, Xi-Yan Hu, An-Ping Liao

Publication date: 13 November 2009

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-007-0369-0

zbMATH Keywords

numerical resultsmatrix equationgeneralized singular value decompositionminimum-norm solutionleast-squares solutioncanonical correlation decomposition

Mathematics Subject Classification ID

Related Items (4)

Solutions to the linear transpose matrix equations and their application in control ⋮ Parametric Solutions to the Generalized Discrete Yakubovich-Transpose Matrix Equation ⋮ Closed-form solutions to the nonhomogeneous Yakubovich-transpose matrix equation ⋮ A computational framework of gradient flows for general linear matrix equations

Cites Work

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• Computing the CS decomposition of a partitioned orthonormal matrix
• Symmetric solutions of linear matrix equations by matrix decompositions
• On solutions of matrix equation \(AXB+CYD=F\)
• State covariance assignment problem with measurement noise: A unified approach based on a symmetric matrix equation
• Perturbation analysis of the canonical correlations of matrix pairs
• The constrained solutions of two matrix equations
• Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
• Linear matrix equations from an inverse problem of vibration theory
• Least-square solutions for inverse problems of centrosymmetric matrices
• Nonnegative definite and positive definite solutions to the matrix equationAXA^*=B
• Towards a Generalized Singular Value Decomposition
• Assigning controllability and observability Gramians in feedback control
• The Equations A^TX\pm X^TA=B
• Inverse scattering via Heisenberg's uncertainty principle
• Least Squares Solution of Matrix Equation $AXB^* + CYD^* = E$
• Best Approximate Solution of Matrix Equation AXB+CYD=E

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