Abstract

Through Taylor’s expansions and a thorough analysis of the necessary and sufficient conditions that will entail for fixed point and Newton’s iterative methods to be of higher order convergence in Banach space, we are able to present a unified way to make these methods faster. Numerical examples illustrate the theoretical results.

中文翻译：

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Banach空间中的高阶不动点和牛顿法

摘要

通过泰勒的展开以及对定点和牛顿迭代方法在Banach空间中具有更高阶收敛性的必要条件和充分条件的透彻分析，我们能够提出使这些方法更快的统一方法。数值例子说明了理论结果。