On convergence of a new secant-like method for solving nonlinear equations

In this paper, we prove that the order of a new secant-like method presented recently with the so-called order of 2.618 is only 2.414. Some mistakes in the derivation leading to such a conclusion are pointed out. Meanwhile, under the assumption that the second derivative of the involved function is...

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Veröffentlicht in:	Applied mathematics and computation 2010-09, Vol.217 (2), p.583-589
Hauptverfasser:	Ren, Hongmin, Wu, Qingbiao, Bi, Weihong
Format:	Artikel
Sprache:	eng
Schlagworte:	Convergence Convergence order Derivation Derivatives Error estimate Errors Estimates Exact sciences and technology Generalized Fibonacci sequence Iterative method Mathematical analysis Mathematical models Mathematics Nonlinear equations Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use Secant-like method
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Zusammenfassung:	In this paper, we prove that the order of a new secant-like method presented recently with the so-called order of 2.618 is only 2.414. Some mistakes in the derivation leading to such a conclusion are pointed out. Meanwhile, under the assumption that the second derivative of the involved function is bounded, the convergence radius of the secant-like method is given, and error estimates matching its convergence order are also provided by using a generalized Fibonacci sequence.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2010.05.092