Newton’s Method

Alexander J. Zaslavski
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Alexander J. Zaslavski: The Technion – Israel Institute of Technology

Chapter Chapter 16 in Numerical Optimization with Computational Errors, 2016, pp 265-296 from Springer

Abstract: Abstract In this chapter we study the convergence of Newton’s method for nonlinear equations and nonlinear inclusions in a Banach space. Nonlinear mappings, which appear in the right-hand side of the equations, are not necessarily differentiable. Our goal is to obtain an approximate solution in the presence of computational errors. In order to meet this goal, in the case of inclusions, we study the behavior of iterates of nonexpansive set-valued mappings in the presence of computational errors.

Keywords: Nonlinear Inclusions; Computational Errors; Nonempty Open Subset; Frechet Derivative; Continuous Linear Operator (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-30921-7_16

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DOI: 10.1007/978-3-319-30921-7_16

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