Local Cr Stability for Iterative Roots of Orientation‐Preserving Self‐Mappings on the Interval

Yingying Zeng

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: Stability of iterative roots is important in their numerical computation. It is known that under some conditions iterative roots of orientation‐preserving self‐mappings are both globally C0 stable and locally C1 stable but globally C1 unstable. Although the global C1 instability implies the general global Cr (r ≥ 2) instability, the local C1 stability does not guarantee the local Cr (r ≥ 2) stability. In this paper we generally prove the local Cr (r ≥ 2) stability for iterative roots. For this purpose we need a uniform estimate for the approximation to the conjugation in Cr linearization, which is given by improving the method used for the C1 case.

Date: 2014
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https://doi.org/10.1155/2014/743032

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:743032

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