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Eighth-Order Iterative Methods without Derivatives for Solving Nonlinear Equations
Author
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-09-06
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
A new family of eighth-order derivative-free methods for solving nonlinear equations is presented.
It is proved that these methods have the convergence order of eight.
These new methods are derivative-free and only use four evaluations of the function per iteration.
In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture.
Kung and Traub conjectured that the multipoint iteration methods, without memory based on n evaluations, could achieve optimal convergence order 2n−1.
Thus, we present new derivative-free methods which agree with Kung and Traub conjecture for n=4.
Numerical comparisons are made to demonstrate the performance of the methods presented.
American Psychological Association (APA)
Thukral, Rajinder. 2011. Eighth-Order Iterative Methods without Derivatives for Solving Nonlinear Equations. ISRN Applied Mathematics،Vol. 2011, no. 2011, pp.1-12.
https://search.emarefa.net/detail/BIM-491127
Modern Language Association (MLA)
Thukral, Rajinder. Eighth-Order Iterative Methods without Derivatives for Solving Nonlinear Equations. ISRN Applied Mathematics No. 2011 (2011), pp.1-12.
https://search.emarefa.net/detail/BIM-491127
American Medical Association (AMA)
Thukral, Rajinder. Eighth-Order Iterative Methods without Derivatives for Solving Nonlinear Equations. ISRN Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-12.
https://search.emarefa.net/detail/BIM-491127
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-491127