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- W1497188405 abstract "Abstract We use inexact Newton-like iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton-like iterates at each stage is very expensive in general. That is why we consider inexact Newton-like methods, where the Newton- like equations are solved only approximately and in some unspecified manner. In the elegant paper [6] natural assumptions under which the forcing sequence is uniformly less than one were given based on the first-Fréchet derivative of the operator involved in the special case of inexact Newton iterates. Here, we use assumptions on the first and second Fréchet-derivative. This way, we essentially reproduce all results found earlier but for inexact Newton-like iterates. However, our upper error bounds on the distances involved are smaller Keywords: Inexact Newton-like methodBanach spaceforcing sequenceFréchet-derivativesuperlinearstrongconvergence" @default.
- W1497188405 created "2016-06-24" @default.
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- W1497188405 date "1999-01-01" @default.
- W1497188405 modified "2023-10-16" @default.
- W1497188405 title "Relations between forcing sequences and inexact newton-like iterates in banach space" @default.
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- W1497188405 doi "https://doi.org/10.1080/00207169908804804" @default.
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