Abstract
The asymptotic rate of convergence of an optimal Chebyshev semiiterative method for solving a real and nonsymmetric linear system x =T x + c can be improved by the related (2,2)-step iterative methods under certain conditions. The condition for which a Chebyshev method asymptotically optimal for an elliptic region is also asymptotically optimal for a nearly elliptic region is presented. Thus a (2,2)-step method is asymptotically superior to the Chebyshev method asymtotically optimal for a nearly elliptic region under certain conditions. A numerical example illustrates our results.
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