Optimal Steffensen-type methods with eighth order of convergence

This paper proposes two classes of three-step without memory iterations based on the well known second-order method of Steffensen. Per computing step, the methods from the developed classes reach the order of convergence eight using only four evaluations, while they are totally free from derivative...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 62; no. 12; pp. 4619 - 4626
Main Authors Soleymani, F., Karimi Vanani, S.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2011
Subjects
Computation
Computer simulation
Convergence
Derivative-free iterations
Derivatives
Efficiency index
Iterative methods
Kung–Traub conjecture
Mathematical models
Optimization
Root
Steffensen-type methods
Kung–Traub conjecture
Derivative-free iterations
Root
Efficiency index
Steffensen-type methods
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Summary:This paper proposes two classes of three-step without memory iterations based on the well known second-order method of Steffensen. Per computing step, the methods from the developed classes reach the order of convergence eight using only four evaluations, while they are totally free from derivative evaluation. Hence, they agree with the optimality conjecture of Kung–Traub for providing multi-point iterations without memory. As things develop, numerical examples are employed to support the underlying theory developed for the contributed classes of optimal Steffensen-type eighth-order methods.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.10.047