Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-08
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
Steffensen-type methods are practical in solving nonlinear equations.
Since, such schemes do not need derivative evaluation per iteration.
Hence, this work contributes two new multistep classes of Steffensen-type methods for finding the solution of the nonlinear equation f(x)=0.
New techniques can be taken into account as the generalizations of the one-step method of Steffensen.
Theoretical proofs of the main theorems are furnished to reveal the eighth-order convergence.
Per computing step, the derived methods require only four function evaluations.
Experimental results are also given to add more supports on the underlying theory of this paper as well as lead us to draw a conclusion on the efficiency of the developed classes.
American Psychological Association (APA)
Soleymani, Fazlollah. 2012. Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-509261
Modern Language Association (MLA)
Soleymani, Fazlollah. Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-509261
American Medical Association (AMA)
Soleymani, Fazlollah. Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-509261
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509261