Special least squares solutions of the quaternion matrix equation \(A X = B\) with applications

DOI10.1016/j.amc.2015.08.046zbMath1410.15036OpenAlexW1139739466MaRDI QIDQ670800

Jianli Zhao, Ying Li, Musheng Wei, Fengxia Zhang

Publication date: 20 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.08.046

zbMATH Keywords

real representationMoore-Penrose generalized inverseleast squares solutionquaternion matrix equationcolor image restoration

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)

Related Items (17)

An efficient real representation method for least squares problem of the quaternion constrained matrix equation AXB + CY D = E ⋮ An efficient method for least-squares problem of the quaternion matrix equationX-AX̂B=C ⋮ A general method for solving linear matrix equations of elliptic biquaternions with applications ⋮ Determinantal representations of solutions to systems of quaternion matrix equations ⋮ Least-squares bihermitian and skew bihermitian solutions of the quaternion matrix equationAXB = C ⋮ On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\) ⋮ Direct Methods of Solving Quaternion Matrix Equation Based on STP ⋮ The forward rounding error analysis of the partial pivoting quaternion LU decomposition ⋮ Semi‐tensor product of quaternion matrices and its application ⋮ A new image restoration model associated with special elliptic quaternionic least-squares solutions based on LabVIEW ⋮ Least squares Hermitian problem of a kind of quaternion tensor equation ⋮ Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F) ⋮ New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems ⋮ Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations ⋮ Explicit determinantal representation formulas of \(W\)-weighted Drazin inverse solutions of some matrix equations over the quaternion skew field ⋮ On Hermitian solutions of the reduced biquaternion matrix equation (AXB,CXD) = (E,G) ⋮ Solving the least squares (anti)-Hermitian solution for quaternion linear systems

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