Abstract
Abstract In this paper we investigate theoretically and numerically the new preconditioned method to accelerate over-relaxation (AOR) and succesive over-relaxation (SOR) schemes, which are used to the large sparse linear systems. The iterative method that is usually measured by the convergence rate is an important method for solving large linear equations, so we focus on the convergence rate of the different preconditioned iterative methods. Our results indicate that the proposed new method is highly effective to improve the convergence rate and it is the best one in three preconditioned methods that are revealed in the comparison theorems and numerical experiment.
Highlights
With the development of natural and social sciences, we always encounter some big data problems which are related to the sparse linear equations
In this paper we investigate theoretically and numerically the new preconditioned method to accelerate over-relaxation (AOR) and succesive over-relaxation (SOR) schemes, which are used to the large sparse linear systems
The iterative method that is usually measured by the convergence rate is an important method for solving large linear equations, so we focus on the convergence rate of the di erent preconditioned iterative methods
Summary
With the development of natural and social sciences, we always encounter some big data problems which are related to the sparse linear equations. The iterative method is presented to solve the approximate solution of the large sparse linear equations, and some e ective iterative schemes are developed, such as the Gauss-Seidel method, Jacobi method, AOR method, SOR and SOR-like method [1, 2] etc. The iterative matrix of Gauss-Seidel method [3] for solving the linear system (1) is. In order to improve convergence of the iterative method, AOR iterative scheme is demonstrated [4,5,6]. A preconditioned AOR iterative scheme for systems of linear equations with L-matrics where w and r are real parameters with w ≠. Convergence is dependent on the iteration matrix and parameters in the iterative methods, and closely related to the changes of the equations themselves.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
