A simplified proof of the Kantorovich theorem for solving equations using telescopic series

Journal of Numerical Analysis and Approximation Theory（2015）

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摘要

We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) [2], [7]. Our results provide at least as precise information on the location of the solution. Numerical examples are also provided in this study.

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关键词

Newton-Kantorovich method,Banach space,majorizing series,telescopic series,Kantorovich theorem

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