scholarly journals Shift-splitting iteration methods for a class of large sparse linear matrix equations

2021 ◽  
Vol 6 (4) ◽  
pp. 4105-4118
Author(s):  
Xu Li ◽  
◽  
Rui-Feng Li
Keyword(s):  
Linear Matrix ◽  
Matrix Equations ◽  
Iteration Methods ◽  
Linear Matrix Equations

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.

scholarly journals The optimal convergence factor of the gradient based iterative algorithm for linear matrix equations

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 607-613 ◽  
Author(s):  
Xiang Wang ◽  
Dan Liao
Keyword(s):  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Convergence Factor ◽  
Gradient Based ◽  
Gradient Type ◽  
And Mathematics ◽  
Computers And Mathematics ◽  
Linear Matrix Equations

A hierarchical gradient based iterative algorithm of [L. Xie et al., Computers and Mathematics with Applications 58 (2009) 1441-1448] has been presented for finding the numerical solution for general linear matrix equations, and the convergent factor has been discussed by numerical experiments. However, they pointed out that how to choose a best convergence factor is still a project to be studied. In this paper, we discussed the optimal convergent factor for the gradient based iterative algorithm and obtained the optimal convergent factor. Moreover, the theoretical results of this paper can be extended to other methods of gradient-type based. Results of numerical experiments are consistent with the theoretical findings.

Matrix completions for linear matrix equations

2017 ◽  
Vol 10 (5) ◽  
pp. 781-799
Author(s):  
Geoffrey Buhl ◽  
Elijah Cronk ◽  
Rosa Moreno ◽  
Kirsten Morris ◽  
Dianne Pedroza ◽  
...  
Keyword(s):  
Linear Matrix ◽  
Matrix Equations ◽  
Linear Matrix Equations
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