Abstract
A necessary and sufficient condition is given in order that a certain iterative method converges to a solution of a nonlinear equation. Furthermore, a criterion is obtained for finding existence and nonexistence domains of solutions for the same equation. The obtained results generalize and deepen those of Kantorovich [4], Rheinbt [6] and Dennis [2] for Newton’s and Newton-like methods.
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References
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© 1988 Springer Basel AG
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Chen, X., Yamamoto, T. (1988). A Necessary and Sufficient Condition for the Convergence of Certain Iterative Methods for Nonlinear Equations. In: Agarwal, R.P., Chow, Y.M., Wilson, S.J. (eds) Numerical Mathematics Singapore 1988. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 86. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6303-2_8
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DOI: https://doi.org/10.1007/978-3-0348-6303-2_8
Publisher Name: Birkhäuser, Basel
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