Semiconvergence of extrapolated iterative method for singular linear systems
نویسنده
چکیده
In this paper, we discuss convergence of the extrapolated iterative methods for solving singular linear systems. A general principle of extrapolation is presented. The semiconvergence of an extrapolated method induced by a regular splitting and a nonnegative splitting is proved whenever the coe cient matrix A is a singular M -matrix with ‘property c’ and an irreducible singular M -matrix, respectively. Since the (generalized, block) JOR and AOR methods are respectively the extrapolated methods of the (generalized, block) Jacobi and SOR methods, so the semiconvergence of the (generalized, block) JOR and AOR methods for solving general singular systems are proved. Furthermore, the semiconvergence of the extrapolated power method, the (block) JOR, AOR and SOR methods for solving Markov chains are discussed. c © 1999 Elsevier Science B.V. All rights reserved.
منابع مشابه
Semiconvergence of Alternating Iterative Methods for Singular Linear Systems
In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained. Keywords—Alternating iterative method; Semiconvergence; Singular matrix.
متن کاملOn the semiconvergence of additive and multiplicative splitting iterations for singular linear systems
Keywords: Additive/multiplicative splitting iteration method Singular linear systems Hermitian matrix Semiconvergence a b s t r a c t In this paper, we investigate the additive, multiplicative and general splitting iteration methods for solving singular linear systems. When the coefficient matrix is Hermitian, the semiconvergence conditions are proposed, which generalize some results of Bai [Z....
متن کاملParallel multisplitting methods for singular linear systems
In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example. Keywords—singular H-matrix, linear systems, ...
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 کاملAn Iterative Method for Symmetric Positive Semidefinite Linear System of Equations
In this paper, a new two-step iterative method for solving symmetric positive semidefinite linear system of equations is presented. A sufficient condition for the semiconvergence of the method is also given. Some numerical experiments are presented to show the efficiency of the proposed method. AMS Subject Classification : 65F10.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 156 شماره
صفحات -
تاریخ انتشار 2004