![](/images/graphics-bg.png)
Computing Simple Roots by an Optimal Sixteenth-Order Class
Joint Authors
Soleymani, Fazlollah
Salmani, H.
Shateyi, Stanford
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-08
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The problem considered in this paper is to approximate the simple zeros of the function f(x) by iterative processes.
An optimal 16th order class is constructed.
The class is built by considering any of the optimal three-step derivative-involved methods in the first three steps of a four-step cycle in which the first derivative of the function at the fourth step is estimated by a combination of already known values.
Per iteration, each method of the class reaches the efficiency index 165≈1.741, by carrying out four evaluations of the function and one evaluation of the first derivative.
The error equation for one technique of the class is furnished analytically.
Some methods of the class are tested by challenging the existing high-order methods.
The interval Newton's method is given as a tool for extracting enough accurate initial approximations to start such high-order methods.
The obtained numerical results show that the derived methods are accurate and efficient.
American Psychological Association (APA)
Soleymani, Fazlollah& Shateyi, Stanford& Salmani, H.. 2012. Computing Simple Roots by an Optimal Sixteenth-Order Class. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-1029060
Modern Language Association (MLA)
Soleymani, Fazlollah…[et al.]. Computing Simple Roots by an Optimal Sixteenth-Order Class. Journal of Applied Mathematics No. 2012 (2012), pp.1-13.
https://search.emarefa.net/detail/BIM-1029060
American Medical Association (AMA)
Soleymani, Fazlollah& Shateyi, Stanford& Salmani, H.. Computing Simple Roots by an Optimal Sixteenth-Order Class. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-1029060
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1029060