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- Title
Local C<sub>r</sub> Stability for Iterative Roots of Orientation-Preserving Self-Mappings on the Interval.
- Authors
Yingying Zeng
- 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 Cr1 linearization, which is given by improving the method used for the C1 case.
- Subjects
ITERATIVE methods (Mathematics); ROOTS of equations; NUMERICAL analysis; APPROXIMATION theory; LINEAR systems
- Publication
Journal of Applied Mathematics, 2014, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2014/743032