Numerical solution of SOR iterative method for fuzzy Fredholm integral equations of second kind

In this paper, we deal with the application of Successive Over-Relaxation (SOR) iterative method for solving fuzzy Fredholm integral equations of the second kind (FFIE-2). In addition to that, we apply the trapezoidal rule to derive the approximate solution of FFIE-2 which consists of a system of integral equations. Next, the approximate equation is used to develop a system of linear equations. Then, we consider SOR iterative method to solve the generated system of linear equations. Next, SOR iterative method is implemented on some numerical examples. Finally, the numerical results is discussed in details by comparing the number of iterations, the computational time, and the Hausdorff distance to analyze the performance of proposed method. Based on the numerical results obtained from all the numerical examples by using Gauss-Seidel (GS) and SOR methods, it can be pointed out that SOR method is more efficient than the GS method

An Implicit Partial Pivoting Gauss Elimination Algorithm for Linear System of Equations with Fuzzy Parameters

This paper considers the solution of fully fuzzy linear system (FFLS) by first reducing the system to crisp linear system. The novelty of this article lies in the application of Gauss elimination procedure with implicit partial pivoting to FFLS. The method is presented in detail and we use the Matlab software for implementing the algorithm. Numerical examples are illustrated to demonstrate the efficiency of the variant of Gauss elimination method for solving FFLS. Keywords: fully fuzzy linear system, fuzzy number, gauss elimination, partial pivoting, implici

Numerical Solution of Interval and Fuzzy System of Linear Equations

A system of linear equations, in general is solved in open literature for crisp unknowns, but in actual case the parameters (coefficients) of the system of linear equations contain uncertainty and are less crisp. The uncertainties may be considered in term of interval or fuzzy number. In this paper, a detail of study of linear simultaneous equations with interval and fuzzy parameter (triangular and trapezoidal) has been performed. New methods have been proposed for solving such systems. First, the methods have been tested for known problems viz. a circuit analysis solved in the literature and the results are found to be in good agreement with the present. Next more example problems are solved using the proposed methods to strengthen confidence on these new methods. The solutions of the example problems clearly show the efficacy and reliability of the proposed method(s)

A new computational method for solving fully fuzzy nonlinear matrix equations

Multi formulations and computational methodologies have been suggested to extract solution of fuzzy nonlinear programming problems. However, in some cases the methods which have been utilised in order to find the solution of these problems involve greater complexity. On the basis of the mentioned reason, the current research work is intended towards introduction of a simple method for finding the fuzzy optimal solution related to fuzzy nonlinear issues. The proposed method is validated and is confirmed to be applicable by suggesting some demonstrated examples. The results confirm that the proposed method is so easy to understand and to apply for solving fully fuzzy nonlinear system (FFNS)

SOR Iterative Method with Simpson’s 1/3 Rule for the Numerical Solution of Fuzzy Second Kind Fredholm Integral Equations

In this study, we present the application of Successive Over-Relaxation (SOR) iterative method to solve fuzzy Fredholm integral equations of the second kind (FFIE-2). In addition to that, the Simpson’s 1/3 quadrature rule is applied to derive the approximate solution of FFIE-2. Then, we use the approximate equation to generate a system of linear equations. Next, SOR iterative method is introduced to solve the generated system of linear equations. Moreover, we conduct some numerical examples to illustrate the applicability of the SOR iterative method. Finally, we discuss the efficiency of the proposed method by comparing the number of iterations, computational time and Hausdorff distance. Based on the numerical results, we conclude that SOR method is better than Jacobi and Gauss-Seidel iterative methods

Job Scheduling Using successive Linear Programming Approximations of a Sparse Model

EuroPar 2012In this paper we tackle the well-known problem of scheduling a collection of parallel jobs on a set of processors either in a cluster or in a multiprocessor computer. For the makespan objective, i.e., the completion time of the last job, this problem has been shown to be NP-Hard and several heuristics have already been proposed to minimize the execution time. We introduce a novel approach based on successive linear programming (LP) approximations of a sparse model. The idea is to relax an integer linear program and use lp norm-based operators to force the solver to find almost-integer solutions that can be assimilated to an integer solution. We consider the case where jobs are either rigid or moldable. A rigid parallel job is performed with a predefined number of processors while a moldable job can define the number of processors that it is using just before it starts its execution. We compare the scheduling approach with the classic Largest Task First list based algorithm and we show that our approach provides good results for small instances of the problem. The contributions of this paper are both the integration of mathematical methods in the scheduling world and the design of a promising approach which gives good results for scheduling problems with less than a hundred processors