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- W2980022323 abstract "Globalization concepts for Newton-type iteration schemes are widely used when solving nonlinear problems numerically. Most of these schemes are based on a predictor/corrector step size methodology with the aim of steering an initial guess to a zero of $f$ without switching between different attractors. In doing so, one is typically able to reduce the chaotic behavior of the classical Newton-type iteration scheme. In this note we propose a globalization methodology for general Newton-type iteration concepts which changes into a simplified Newton iteration as soon as the transformed residual of the underlying function is small enough. Based on Banach's fixed-point theorem, we show that there exists a neighborhood around a suitable iterate $x_{n}$ such that we can steer the iterates---without any adaptive step size control but using a simplified Newton-type iteration within this neighborhood---arbitrarily close to an exact zero of $f$. We further exemplify the theoretical result within a global Newton-type iteration procedure and discuss further an algorithmic realization. Our proposed scheme will be demonstrated on a low-dimensional example thereby emphasizing the advantage of this new solution procedure." @default.
- W2980022323 created "2019-10-18" @default.
- W2980022323 creator A5059931868 @default.
- W2980022323 date "2019-10-08" @default.
- W2980022323 modified "2023-10-03" @default.
- W2980022323 title "A Global Newton-Type Scheme Based on a Simplified Newton-Type Approach" @default.
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