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Comput."],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 <jats:italic>f<\/jats:italic> 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\u2019s fixed-point theorem, we show that there exists a neighborhood around a suitable iterate <jats:inline-formula><jats:alternatives><jats:tex-math>$$x_{n}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>x<\/mml:mi>\n                    <mml:mi>n<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such that we can steer the iterates\u2014without any adaptive step size control but using a simplified Newton-type iteration within this neighborhood\u2014arbitrarily close to an exact zero of <jats:italic>f<\/jats:italic>. 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.<\/jats:p>","DOI":"10.1007\/s12190-020-01393-w","type":"journal-article","created":{"date-parts":[[2020,7,9]],"date-time":"2020-07-09T10:05:31Z","timestamp":1594289131000},"page":"321-334","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A global Newton-type scheme based on a simplified Newton-type approach"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4182-0027","authenticated-orcid":false,"given":"Mario","family":"Amrein","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,9]]},"reference":[{"key":"1393_CR1","unstructured":"Amrein, M.: Adaptive Newton-Type Schemes Based on Projections, Tech. 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