Abstract
The semi-iterative method (SIM) is applied to the hyper-power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi-iterative–hyper-power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.
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