Show simple item record

dc.contributor.authorRhee, Min Surp
dc.contributor.authorKim, Young Ik
dc.contributor.authorNeta, Beny
dc.date.accessioned2017-12-07T15:59:29Z
dc.date.available2017-12-07T15:59:29Z
dc.date.issued2018
dc.identifier.citationM.S. Rhee, Y.I. Kim, B. Neta, "An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points," International Journal of Computer Mathematics, (2017), 38 p.en_US
dc.identifier.urihttp://hdl.handle.net/10945/56409
dc.descriptionThe article of record as published may be found at http://dx.doi.org/10.1080/00207160.2017.1367387en_US
dc.description.abstractIn this paper, we not only develop an optimal class of three-step eighth-order methods with higher order weight functions employed in the second and third sub-steps, but also investigate their dynamics underlying the purely imaginary extraneous fixed points. Their theoretical and computational properties are fully described along with a main theorem stating the order of convergence and the asymptotic error constant as well as extensive studies of special cases with rational weight functions. A number of numerical examples are illustrated to confirm the underlying theoretical development. Besides, to show the convergence behaviour of global character, fully explored is the dynamics of the proposed family of eighth-order methods as well as an existing competitive method with the help of illustrative basins of attraction.en_US
dc.format.extent38 p.en_US
dc.publisherTaylor & Francisen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleAn optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed pointsen_US
dc.typeArticleen_US
dc.contributor.corporateNaval Postgraduate School (U.S.)en_US
dc.contributor.departmentApplied Mathematicsen_US
dc.subject.authorEighth-order convergenceen_US
dc.subject.authorWeight functionen_US
dc.subject.authorAsymptotic error constanten_US
dc.subject.authorEfficiency indexen_US
dc.subject.authorPurely imagninary extraneous fixed pointen_US
dc.subject.authorBasin of attractionen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record