Abstract
In this contribution we generalize Newton’s method and related methods for the solution of fixed point problems. We replace the linear approximations to a given nonlinear operator which result from differentiability assumptions by arbitrary “tangent” mappings. Therefore our iteration algorithms apply to nondifferentiable operators. As these tangent mappings may also be chosen affine, we include the differentiable case, thereby extending some recent results in [2].
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Literature
J. Dieudonné: Foundations of Modern Analysis. Academic Press, New York, 1960.
L.B. Rall: Convergence of Stirling’s Method in Banach Spaces. Aequationes Math. 12 (1975), 12–20.
R.A. Tapia: The Differentiation and Integration of Nonlinear Operators, Nonlinear Functional Analysis and Applications, L.B. Rall, ed., Academic Press, New York, 1971, pp. 45–102.
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© 1976 Springer-Verlag Berlin · Heidelberg
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Gwinner, J. (1976). Generalized Stirling-Newton Methods. In: Oettli, W., Ritter, K. (eds) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46329-7_9
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DOI: https://doi.org/10.1007/978-3-642-46329-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07616-2
Online ISBN: 978-3-642-46329-7
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