2005•Numerical Linear Algebra with ApplicationsRequires access

The semi-iterative method applied to the hyper-power iteration

Xuzhou Chen, Robert E. Hartwig

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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Key concepts: Power iteration, Mathematics, Rate of convergence, Iterative method, Convergence (economics), Rayleigh quotient iteration, Applied mathematics, Preconditioner