scholarly journals Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Approximate Solution ◽  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Existence Condition ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Arithmetic Operations ◽  
Fuzzy Matrix ◽  
Fuzzy Solution ◽  
Linear Matrix Equations

The fuzzy matrix equationsA~⊗X~⊗B~=C~in whichA~,B~, andC~arem×m,n×n, andm×nnonnegative LR fuzzy numbers matrices, respectively, are investigated. The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. In addition, the existence condition of nonnegative fuzzy solution is discussed. Two examples are calculated to illustrate the proposed method.

scholarly journals Solving Complex Fuzzy Linear Matrix Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yirong Sun ◽  
Junyang An ◽  
Xiaobin Guo
Keyword(s):  
Matrix Equation ◽  
Fuzzy Numbers ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Linear Matrix Equation ◽  
Fuzzy Matrix ◽  
System Of Matrix Equations ◽  
Fuzzy Solution ◽  
Simplified Procedures ◽  
Linear Matrix Equations

In this paper, a kind of complex fuzzy linear matrix equation A X ˜ B = C ˜ , in which C ˜ is a complex fuzzy matrix and A and B are crisp matrices, is investigated by using a matrix method. The complex fuzzy matrix equation is extended into a crisp system of matrix equations by means of arithmetic operations of fuzzy numbers. Two brand new and simplified procedures for solving the original fuzzy equation are proposed and the correspondingly sufficient condition for strong fuzzy solution are analysed. Some examples are calculated in detail to illustrate our proposed method.

scholarly journals Approximate Solution of LR Fuzzy Sylvester Matrix Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Matrix Equation ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Existence Condition ◽  
Sylvester Matrix Equation ◽  
Fuzzy Matrix ◽  
Sylvester Matrix ◽  
Fuzzy Linear System

The fuzzy Sylvester matrix equationAX~+X~B=C~in whichA,Barem×mandn×ncrisp matrices, respectively, andC~is anm×nLR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

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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