Abstract
Are Fixed Point Methods effective ? In this paper, we discuss the efficiency of modern fixed point methods. Our investigations concentrate on two special situations: First, we consider problems with “well — behaved” functions and demonstrate that the efficiency in such cases is comparable to that of Newton’s method. In the second place, we consider “wild” functions such that Newton’s method cannot even be formulated, to say nothing of good convergence results. Even in such situations fixed point methods may have linear convergence properties. To sum up, modern fixed point methods have (in contrast to older formulations) convergence properties which make them a valuable tool in numerical analysis.
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Cromme, L.J. (1980). Sind Fixpunktverfahren Effektiv?. In: Collatz, L., Meinardus, G., Wetterling, W. (eds) Konstruktive Methoden der finiten nichtlinearen Optimierung. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6322-3_3
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DOI: https://doi.org/10.1007/978-3-0348-6322-3_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6323-0
Online ISBN: 978-3-0348-6322-3
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