![](/images/graphics-bg.png)
New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-03
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 of 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. 2012. New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-476053
Modern Language Association (MLA)
Thukral, Rajinder. New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-12.
https://search.emarefa.net/detail/BIM-476053
American Medical Association (AMA)
Thukral, Rajinder. New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-476053
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-476053