Local convergence of the Newton’s method in two step nilpotent Lie groups
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Bibliographic record
Abstract
In this paper, we consider N, a simply connected two-step nilpotent Lie group with N , its corresponding (two-step nilpotent) Lie algebra, and we study Newton's method for solving the equation f (x) = 0, where f : N N is a mapping. Under certain generalized Lipschitz condition, we obtain the convergence radius of Newton's method and the estimation of the uniqueness ball of the zero point of f . Some applications to special cases including Kantorovich's condition and -condition are provided. The determination of an approximate zero point of an analytic mapping is also presented.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
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| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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