#GAUSS SEIDEL METHODS SOFTWARE#

Simple numerical examples are also given, and we show that the convergence rate of the proposed method is better than that of the optimum SOR. In addition, the convergence and comparison theorems of the proposed method are established. In the present paper, in order to deal with this drawback, we propose a new preconditioner. Since these preconditioners are constructed from the elements of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row of matrix A. (published under the terms of the Creative Commons Attribution 4.In recent years, a number of preconditioners have been applied to linear systems ]. In a Gauss-Seidel type method for DNCPs, by first guessing a solution of the differential system, we can solve the complementarity system and then with the. * Author to whom correspondence should be addressed Keywords: normal equations, block GaussвЂ“Seidel method, Cholesky method, linear algebraic systems of large dimension. The results of numerical experimentation demonstrating the effectiveness of the proposed approach are given. Normal equations arising at each iteration of GaussвЂ“Seidel method, have a relatively low dimension compared to the original system. In this paper, we propose a procedure to replace the matrix pseudo-solutions to the problem of normal systems of equations by Cholesky. Solve the system of equations 10x - 5y - 2z 3, 4x - 10y + 3z -3, x + 6y + 10z -3 by Gauss Seidel method. We know that finding the pseudoinverse is a difficult computational procedure. The disadvantage of the block GaussвЂ“Seidel method for production systems is the fact that it is necessary to calculate the pseudoinverse matrix for each iteration. One of the effective approaches that improve the speed of convergence of the iterative GaussвЂ“Seidel method for normal systems of equations, is to use its version of the block. However, universal preconditioner for all applications does not exist. To increase the speed of convergence of iterative methods based on normal equations systems, for solving ill-conditioned problems currently different preconditioners options are used that reduce the condition number of the original system of equations. This fact has a negative impact on the rate of convergence of iterative methods based on normal equations systems. The main disadvantage of methods based on normal equations systems is the fact that the condition number of the normal system is equal to the square of the condition number of the original problem. In this method firstly we are taking the initial guesses of voltage values so that we get value of the particular variables by putting the values of initial guesses into equation. This method is an iterative method used to solve the non-linear equations in power flow studies. This article focuses on the modification of the block option Gauss-Seidel method for normal systems of equations, which is a sufficiently effective method of solving generally overdetermined, systems of linear algebraic equations of high dimensionality. The Gauss- Seidel method is modification of the Gauss-iteration method. Samara State Technical University, Samara, 443100, Russian Federation On a computer implementation of the block GaussвЂ“Seidel method

#GAUSS SEIDEL METHODS SOFTWARE#

Mathematical Modeling, Numerical Methods and Software Complexes

Gauss seidel methods