Local convergence analysis of Inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds

Tiberio Bittencourt and Orizon Pereira Ferreira

Applied Mathematics and Computation, 2015, vol. 261, issue C, 28-38

Abstract: A local convergence analysis of Inexact Newton’s method with relative residual error tolerance for finding a singularity of a differentiable vector field defined on a complete Riemannian manifold, based on majorant principle, is presented in this paper. We prove that under local assumptions, the Inexact Newton method with a fixed relative residual error tolerance converges Q linearly to a singularity of the vector field under consideration. Using this result we show that the Inexact Newton method to find a zero of an analytic vector field can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieves the classical local theorem on the Newton method in Riemannian context.

Keywords: Inexact Newton’s method; Majorant principle; Local convergence analysis; Riemannian manifold (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:261:y:2015:i:c:p:28-38

DOI: 10.1016/j.amc.2015.03.080

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