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

Yingying Zeng

Journal of Applied Mathematics, 2014, vol. 2014, 1-8

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 stable and locally stable but globally unstable. Although the global instability implies the general global ( ) instability, the local stability does not guarantee the local ( ) stability. In this paper we generally prove the local ( ) stability for iterative roots. For this purpose we need a uniform estimate for the approximation to the conjugation in linearization, which is given by improving the method used for the case.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:743032

DOI: 10.1155/2014/743032

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