黎曼流形中Mann迭代法的Kantorovich定理

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2024-06-29 DOI:10.1007/s40306-024-00541-9

Babita Mehta, P. K. Parida, Sapan Kumar Nayak

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引用次数: 0

摘要

本文利用Kantorovich定理研究了Mann迭代法在连通完备黎曼流形下的收敛性。我们还提供了Mann方法在二维球面上寻找奇点的算法\(S^2\)。最后给出了一个算例，说明Mann方法的收敛性优于Newton方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Kantorovich’s Theorem on Mann’s Iteration Method in Riemannian Manifold

Convergence analysis of Mann’s iteration method using Kantorovich’s theorem in the context of connected and complete Riemannian manifolds has been examined in this paper. We also provide an algorithm for Mann’s method to find a singularity in a two dimensional sphere \(S^2\). Finally, we provide an example that shows the better convergence result of Mann’s method in comparison to that of Newton’s method.

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来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.