Geometric Construction of Eighth-Order Optimal Families of Ostrowski’s Method
Joint Authors
Motsa, Sandile Sydney
Behl, Ramandeep
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-26
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Based on well-known fourth-order Ostrowski’s method, we proposed many new interesting optimal families of eighth-order multipoint methods without memory for obtaining simple roots.
Its geometric construction consists in approximating fn′ at zn in such a way that its average with the known tangent slopes fn′ at xn and yn is the same as the known weighted average of secant slopes and then we apply weight function approach.
The adaptation of this strategy increases the convergence order of Ostrowski's method from four to eight and its efficiency index from 1.587 to 1.682.
Finally, a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal eighth-order methods available in the literature.
It is found that they are very useful in high precision computations.
Further, it is also noted that larger basins of attraction belong to our methods although the other methods are slow and have darker basins while some of the methods are too sensitive upon the choice of the initial value.
American Psychological Association (APA)
Behl, Ramandeep& Motsa, Sandile Sydney. 2015. Geometric Construction of Eighth-Order Optimal Families of Ostrowski’s Method. The Scientific World Journal،Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1078926
Modern Language Association (MLA)
Behl, Ramandeep& Motsa, Sandile Sydney. Geometric Construction of Eighth-Order Optimal Families of Ostrowski’s Method. The Scientific World Journal No. 2015 (2015), pp.1-11.
https://search.emarefa.net/detail/BIM-1078926
American Medical Association (AMA)
Behl, Ramandeep& Motsa, Sandile Sydney. Geometric Construction of Eighth-Order Optimal Families of Ostrowski’s Method. The Scientific World Journal. 2015. Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1078926
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1078926