Least-squares Hermitian problem of complex matrix equation \((AXB,CXD)=(E,F)\)

DOI10.1186/s13660-016-1231-9zbMath1354.65080OpenAlexW2549923627WikidataQ59468569 ScholiaQ59468569MaRDI QIDQ343551

Peng Wang, Shi-Fang Yuan, Xiang-Yun Xie

Publication date: 28 November 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-016-1231-9

zbMATH Keywords

Hermitian matricesdirect methodnumerical experimentmatrix equationMoore-Penrose generalized inverseleast squares solutionminimum norm solution

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Matrix equations and identities (15A24) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (5)

Solution of the symmetric band partial inverse eigenvalue problem for the damped mass spring system ⋮ Solution of the linearly structured partial polynomial inverse eigenvalue problem ⋮ Symmetric least squares solution of a class of Sylvester matrix equations via MINIRES algorithm ⋮ An efficient method for special least squares solution of the complex matrix equation \((AXB,CXD)=(E,F)\) ⋮ An inverse eigenvalue problem in symmetric sparse quadratic model updating

Cites Work

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• Analogs of Cramer's rule for the minimum norm least squares solutions of some matrix equations
• On the Hermitian solutions to a system of adjointable operator equations
• An efficient algorithm for solving general coupled matrix equations and its application
• Least-squares solution with the minimum-norm for the matrix equation \((A\times B,G\times H) = (C,D)\)
• Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions
• Linear matrix equations from an inverse problem of vibration theory
• Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations
• Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm
• Generalized solution sets of the interval generalized Sylvester matrix equation \(\sum_{i=1}^p\mathbf A_iX_i+\sum_{j=1}^qY_j\mathbf B_j=\mathbf C\) and some approaches for inner and outer estimations
• Solvability conditions and general solution for mixed Sylvester equations
• Medical Image Noise Reduction Using the Sylvester–Lyapunov Equation
• Application of ADI Iterative Methods to the Restoration of Noisy Images
• The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices

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