The least-squares solutions of the some matrix equation

2010 ◽  
Author(s):  
Yan-Ping Sheng ◽  
Yi-Hen Yan ◽  
Ru Tian
Keyword(s):  
Least Squares ◽  
Matrix Equation

scholarly journals Classification and approximation of solutions to Sylvester matrix equation

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4261-4280 ◽  
Author(s):  
Bogdan Djordjevic ◽  
Nebojsa Dincic
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Infinitely Many Solutions ◽  
Sylvester Matrix Equation ◽  
Minimal Norm ◽  
Sylvester Matrix

In this paperwesolve Sylvester matrix equation with infinitely-many solutions and conduct their classification. If the conditions for their existence are not met, we provide a way for their approximation by least-squares minimal-norm method.

scholarly journals Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix EquationAXB+CXD=Ewith the Least Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shi-Fang Yuan
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Kronecker Product ◽  
Generalized Inverse ◽  
Complex Representation ◽  
Real Solution ◽  
Quaternion Matrix ◽  
Quaternion Matrices ◽  
Quaternion Matrix Equation ◽  
Product Of Matrices

Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the least norm, and least squares real solution with the least norm of the quaternion matrix equationAXB+CXD=E, respectively.

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