Titlebook: Advances in Iterative Methods for Nonlinear Equations; Sergio Amat,Sonia Busquier Book 2016 Springer International Publishing Switzerland

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Manfred Wick,Paul Lehmann,Wulf Pinggerats are analyzed for the family of Newton-like iterative process. We obtain significant improvements from the study performed. Finally, considerations about the family of iterative processes are done and some numerical examples and applications to boundary-value problem are given.

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2199-3041 ethods.Features accompanying tables and figures.Includes supThis book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynami

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Manfred Wick,Wulf Pinggera,Paul Lehmannss the order, and the development of inverse operators (derivative and divided differences). We also provide a detailed study of a new computational technique to analyze efficiency. Finally, we end the chapter with a consideration of adaptive arithmetic to accelerate computations.

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https://doi.org/10.1007/978-3-319-64774-6In this chapter we study of the Inexact Newton Method in order to solve problems on a Riemannian Manifold. We present standard notation and previous results on Riemannian manifolds. A local convergence study is presented and some special cases are also provided.

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Procalcitonin and New BiomarkersWe present, from the Kantorovich theory for Newton’s method, two variants of the classic Newton-Kantorovich study that allow guaranteeing the semilocal convergence of the method for solving more nonlinear equations.