Comparative study of Symmetric Gauss-Seidel methods and preconditioned Symmetric Gauss-Seidel methods for linear system
نویسندگان
چکیده
This paper deals with the comparative study of preconditioned Symmetric Gauss-Seidel (SGS), New (NSGS), and Parametric (PSGS) methods for solving linear system Ax = b are considered. is precondition type I + S. Convergence properties analyzed standard procedures a numerical experiment undertaken to compare efficiency matrix. Algorithms prepared. MATLAB software used checking computational iterative methods. Results indicate effectiveness preconditioning.
منابع مشابه
Preconditioned Gauss-seidel Iterative Method for Z-matrices Linear Systems
For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (α) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (α) + K̄ (β) as a preconditioner. We present some com...
متن کاملSelf-adaptive Extrapolated Gauss-Seidel Iterative Methods
In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive ...
متن کاملGauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems
We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess ...
متن کاملGeneralized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations
respectively. There are many iterative methods such as GMRES [7] and Bi-CGSTAB [9] algorithms for solving Eq. (1.1) which are more efficient than the Jacobi and Gauss-Seidel methods. However, when these methods are combined with the more efficient methods, for example as a preconditioner, can be quite successful. For example see [4, 6]. It has been proved that if A is a strictly diagonally domi...
متن کاملAn acceleration technique for the Gauss-Seidel method applied to symmetric linear systems
Abstract. A preconditioning technique to improve the convergence of the Gauss-Seidel method applied to symmetric linear systems while preserving symmetry is proposed. The preconditioner is of the form I + K and can be applied an arbitrary number of times. It is shown that under certain conditions the application of the preconditioner a finite number of steps reduces the matrix to a diagonal. A ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Science and Research Archive
سال: 2023
ISSN: ['2582-8185']
DOI: https://doi.org/10.30574/ijsra.2023.8.1.0155