A technique for constructing an initial point for solving a system of linear equations by iterative methods

2002 ◽  
Author(s):  
P.K. Chan
Keyword(s):  
Iterative Methods ◽  
Linear Equations ◽  
Initial Point ◽  
System Of Linear Equations

Certain efficient iterative methods for bipolar fuzzy system of linear equations

2020 ◽  
Vol 39 (3) ◽  
pp. 3971-3985 ◽  
Author(s):  
Muhammad Saqib ◽  
Muhammad Akram ◽  
Shahida Bashir
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Iterative Methods ◽  
Fuzzy Set ◽  
Fuzzy System ◽  
Linear Equations ◽  
Performance Validity ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Iterative Schemes

A bipolar fuzzy set model is an extension of fuzzy set model. We develop new iterative methods: generalized Jacobi, generalized Gauss-Seidel, refined Jacobi, refined Gauss-seidel, refined generalized Jacobi and refined generalized Gauss-seidel methods, for solving bipolar fuzzy system of linear equations(BFSLEs). We decompose n ×  n BFSLEs into 4n ×  4n symmetric crisp linear system. We present some results that give the convergence of proposed iterative methods. We solve some BFSLEs to check the validity, efficiency and stability of our proposed iterative schemes. Further, we compute Hausdorff distance between the exact solutions and approximate solution of our proposed schemes. The numerical examples show that some proposed methods converge for the BFSLEs, but Jacobi and Gauss-seidel iterative methods diverge for BFSLEs. Finally, comparison tables show the performance, validity and efficiency of our proposed iterative methods for BFSLEs.

scholarly journals Convergence of relaxed chaotic parallel iterative methods

1994 ◽  
Vol 50 (1) ◽  
pp. 167-176 ◽  
Author(s):  
Peter E. Kloeden ◽  
Dong-Jin Yuan
Keyword(s):  
Iterative Methods ◽  
Large Scale ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
System Of Linear Equations ◽  
Parallel Iterative Methods ◽  
Parallel Iterative

Sufficient conditions involving uniform multisplittings are established for the convergence of relaxed and AOR versions of asynchronous or chaotic parallel iterative methods for solving a large scale nonsingular system of linear equations Ax = b.

Modified Iterative Methods for Solving Fully Fuzzy Linear Systems

Fuzzy Systems ◽  
2017 ◽  
pp. 55-73
Author(s):  
S. A. Edalatpanah
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Fuzzy System ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Numerical Procedure ◽  
Numerical Results ◽  
System Of Linear Equations ◽  
Iterative Schemes ◽  
Fuzzy Linear Systems

In the present chapter, we give an overview of computational iterative schemes for fuzzy system of linear equations. We also consider fully fuzzy linear systems (FFLS) and demonstrate a class of the existing iterative methods using the splitting approach for calculating the solution. Furthermore, the main aim in this work is to design a numerical procedure for improving this algorithm. Some numerical experiments are illustrated to show the applicability of the methods and to show the efficiency of proposed algorithm, we report the numerical results of large-scaled fuzzy problems.

Modified Iterative Methods for Solving Fully Fuzzy Linear Systems

2017 ◽  
pp. 322-339
Author(s):  
S. A. Edalatpanah
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Fuzzy System ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Numerical Procedure ◽  
Numerical Results ◽  
System Of Linear Equations ◽  
Iterative Schemes ◽  
Fuzzy Linear Systems

In the present chapter, we give an overview of computational iterative schemes for fuzzy system of linear equations. We also consider fully fuzzy linear systems (FFLS) and demonstrate a class of the existing iterative methods using the splitting approach for calculating the solution. Furthermore, the main aim in this work is to design a numerical procedure for improving this algorithm. Some numerical experiments are illustrated to show the applicability of the methods and to show the efficiency of proposed algorithm, we report the numerical results of large-scaled fuzzy problems.

scholarly journals Iterative Methods for Solving a System of Linear Equations in a Bipolar Fuzzy Environment

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 728 ◽  
Author(s):  
Muhammad Akram ◽  
Ghulam Muhammad ◽  
Ali N. A. Koam ◽  
Nawab Hussain
Keyword(s):  
Iterative Methods ◽  
Linear Equations ◽  
Jacobi Method ◽  
System Of Linear Equations ◽  
Linear System Of Equations ◽  
Sor Method ◽  
Fuzzy Environment ◽  
Fuzzy Linear System ◽  
Richardson Method ◽  
Successive Over Relaxation

We develop the solution procedures to solve the bipolar fuzzy linear system of equations (BFLSEs) with some iterative methods namely Richardson method, extrapolated Richardson (ER) method, Jacobi method, Jacobi over-relaxation (JOR) method, Gauss–Seidel (GS) method, extrapolated Gauss-Seidel (EGS) method and successive over-relaxation (SOR) method. Moreover, we discuss the properties of convergence of these iterative methods. By showing the validity of these methods, an example having exact solution is described. The numerical computation shows that the SOR method with ω = 1 . 25 is more accurate as compared to the other iterative methods.

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