scholarly journals A Relaxed Kaczmarz Method for Fuzzy Linear Systems

2021 ◽  
Author(s):  
Ke Wang ◽  
Shijun Zhang ◽  
Shiheng Wang
Keyword(s):  
Linear Systems ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Coefficient Matrix ◽  
Systems Of Equations ◽  
Numerical Examples ◽  
Right Hand ◽  
Kaczmarz Method ◽  
Fuzzy Linear Systems ◽  
Linear Systems Of Equations

Abstract A relaxed Kaczmarz method is presented for solving a class of fuzzy linear systems of equations with crisp coefficient matrix and fuzzy right-hand side. The iterative scheme is established and the convergence theorem is provided. Numerical examples show that the method is effective.

scholarly journals On the solution of fuzzy dual linear systems of equation

2015 ◽  
Vol 4 (2) ◽  
pp. 325
Author(s):  
S. M. Khorasani Kiasari ◽  
L. Abdollahzadeh Ramhormozi
Keyword(s):  
Objective Function ◽  
Linear Systems ◽  
Optimization Problem ◽  
Existence Of Solution ◽  
Systems Of Equations ◽  
Numerical Examples ◽  
Fuzzy Solution ◽  
Fuzzy Linear Systems ◽  
Linear Systems Of Equations

<p>In this paper the exact, multiple and approximation solutions of Dual fuzzy linear systems of equations(DFLSE) with triangular variable are investigated based on a 1-level expansion. To this end, 1-level of DFLSE are solved for calculating the cores of fuzzy solution and then its spreads are obtained by solving an optimization problem with a special objective function. Finally, the existence of solution of DFLSE is proved in details and some numerical examples are solved to illustrate the accuracy and capability of the method</p>

scholarly journals MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xin Li ◽  
Hao Liu ◽  
Jingfu Zhu
Keyword(s):  
Linear Systems ◽  
Projection Method ◽  
Symmetric Matrix ◽  
Coefficient Matrix ◽  
Projection Methods ◽  
Numerical Examples ◽  
Right Hand ◽  
Symmetric Systems

We consider the MINRES seed projection method for solving multiple right-hand side linear systemsAX=B, whereA∈Rn×nis a nonsingular symmetric matrix,B∈Rn×p. In general, GMRES seed projection method is one of the effective methods for solving multiple right-hand side linear systems. However, when the coefficient matrix is symmetric, the efficiency of this method would be weak. MINRES seed projection method for solving symmetric systems with multiple right-hand sides is proposed in this paper, and the residual estimation is analyzed. The numerical examples show the efficiency of this method.

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