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The Computer Journal 1964 7(2):137-140; doi:10.1093/comjnl/7.2.137
© 1964 by British Computer Society
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The extrapolated modified Aitken iteration method applied to {sigma}1-ordered systems of linear equations

D. J. Evans *

Computing Machine Laboratory, The University, Manchester, UK

The extrapolated Aitken iteration method as applied to {sigma}2-ordered systems of linear equations was proposed and analyzed by Evans (1963), who showed that with a suitable choice of extrapolation factor, together with Chebyshev acceleration, an asymptotic rate of convergence superior to the of S.O.R. may be obtained for certain problems.

The present paper applies the above method to {sigma}1-ordered systems of linear equations, and the analysis concerning the extrapolation and Chebyshev acceleration of the iterative procedure is discussed. The theoretical results derived for the asymptotic rate of convergence for both the {sigma}1 and {sigma}2-orderings are confirmed by numerical examples.


* Computing Machine Laboratory, The University, Manchester 13.


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