da Cunha, Rudnei Dias and Hopkins, Tim (1994) A Comparison of Acceleration Techniques Applied to the Sor Method. In: Cuyt, A., ed. Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications . Springer, Dordrecht, pp. 247260. ISBN 9780792329671. EISBN 9789401109703. (doi:10.1007/9789401109703_21) (KAR id:21200)
PDF
Language: English 

Download this file (PDF/189kB) 

Request a format suitable for use with assistive technology e.g. a screenreader  
Postscript
Language: English 

Download this file (Postscript/671kB) 
Preview 
Request a format suitable for use with assistive technology e.g. a screenreader  
Official URL: https://doi.org/10.1007/9789401109703_21 
Abstract
In this paper we investigate the performance of four different SOR acceleration techniques on a variety of linear systems. Two of these techniques have been proposed by Dancis [1] who uses a polynomial acceleration together with a suboptimal ω. The two other techniques discussed are vector accelerations; the ε algorithm proposed by Wynn [9] and a generalisation of Aitken’s Δ2 algorithm, proposed by GravesMorris [3].
The experimental results show that these accelerations can reduce the amount of work required to obtain a solution and that their rates of convergence are generally less sensitive to the value of ω than the straightforward SOR method. However a poor choice of ω can result in particularly inefficient solutions and more work is required to enable cheap estimates of a effective parameter to be obtained.
Necessary conditions for the reduction in the computational work required for convergence are given for each of the accelerations, based on the number of floatingpoint operations.
It is shown experimentally that the reduction in the number of iterations is related to the separation between the two largest eigenvalues of the SOR iteration matrix for a given ω. This separation influences the convergence of all the acceleration techniques above.
Another important characteristic exhibited by these accelerations is that even if the number of iterations is not reduced significantly compared to the SOR method, they are competitive in terms of number of floatingpoint operations used and thus they reduce the overall computational workload.
Item Type:  Book section 

DOI/Identification number:  10.1007/9789401109703_21 
Uncontrolled keywords:  Sor; acceleration 
Subjects:  Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming, 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing 
Depositing User:  Mark Wheadon 
Date Deposited:  13 Aug 2009 20:52 UTC 
Last Modified:  27 Nov 2023 10:01 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/21200 (The current URI for this page, for reference purposes) 
 Link to SensusAccess
 Export to:
 RefWorks
 EPrints3 XML
 BibTeX
 CSV
 Depositors only (login required):