An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence
Joint Authors
Sharma, Rajni
Sharma, Janak Raj
Source
Advances in Numerical Analysis
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-18
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We derive a family of eighth-order multipoint methods for the solution of nonlinear equations.
In terms of computational cost, the family requires evaluations of only three functions and one first derivative per iteration.
This implies that the efficiency index of the present methods is 1.682.
Kung and Traub (1974) conjectured that multipoint iteration methods without memory based on n evaluations have optimal order 2n-1.
Thus, the family agrees with Kung-Traub conjecture for the case n=4.
Computational results demonstrate that the developed methods are efficient and robust as compared with many well-known methods.
American Psychological Association (APA)
Sharma, Rajni& Sharma, Janak Raj. 2012. An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence. Advances in Numerical Analysis،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-464562
Modern Language Association (MLA)
Sharma, Rajni& Sharma, Janak Raj. An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence. Advances in Numerical Analysis No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-464562
American Medical Association (AMA)
Sharma, Rajni& Sharma, Janak Raj. An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence. Advances in Numerical Analysis. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-464562
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-464562