Iterative algorithms for the minimum-norm solution and the least-squares solution of the linear matrix equations

2011 ◽  
Vol 218 (7) ◽  
pp. 3166-3175 ◽  
Author(s):  
Kaifu Liang ◽  
Jianzhou Liu
Keyword(s):  
Least Squares ◽  
Iterative Algorithms ◽  
Linear Matrix ◽  
Minimum Norm ◽  
Matrix Equations ◽  
Minimum Norm Solution ◽  
Least Squares Solution ◽  
Linear Matrix Equations

Least squares solution with the minimum-norm to general matrix equations via iteration

2010 ◽  
Vol 215 (10) ◽  
pp. 3547-3562 ◽  
Author(s):  
Zhao-Yan Li ◽  
Yong Wang ◽  
Bin Zhou ◽  
Guang-Ren Duan
Keyword(s):  
Least Squares ◽  
Minimum Norm ◽  
Matrix Equations ◽  
General Matrix ◽  
Least Squares Solution

scholarly journals A generalized inverse for matrices

1955 ◽  
Vol 51 (3) ◽  
pp. 406-413 ◽  
Author(s):  
R. Penrose
Keyword(s):  
Unique Solution ◽  
Spectral Decomposition ◽  
Generalized Inverse ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Singular Matrix ◽  
Rectangular Matrix ◽  
New Type ◽  
Linear Matrix Equations

This paper describes a generalization of the inverse of a non-singular matrix, as the unique solution of a certain set of equations. This generalized inverse exists for any (possibly rectangular) matrix whatsoever with complex elements. It is used here for solving linear matrix equations, and among other applications for finding an expression for the principal idempotent elements of a matrix. Also a new type of spectral decomposition is given.

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