Chebyshev–Halley’s method on Riemannian manifolds
作者：
Highlights：
•
• We extend the Chebyshev–Halley’s method on Banach spaces to Riemannian manifold.
• A characterization of the convergence under Kantorovich-type conditions is given.
• Results on local uniqueness of solution and error estimates are also given.
• We propose an algorithm to compute singular points of vector fields on the sphere.
摘要
•We extend the Chebyshev–Halley’s method on Banach spaces to Riemannian manifold.•A characterization of the convergence under Kantorovich-type conditions is given.•Results on local uniqueness of solution and error estimates are also given.•We propose an algorithm to compute singular points of vector fields on the sphere.
论文关键词：Riemannian manifolds,Kantorovich-type conditions,Newton and Chebyshev–Halley’s methods
论文评审过程：Received 10 November 2016, Revised 6 November 2017, Available online 28 December 2017, Version of Record 16 January 2018.
论文官网地址：https://doi.org/10.1016/j.cam.2017.12.019
