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Author Kung, H. T. ♦ Traub, J. F.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1974
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract The problem is to calculate a simple zero of a nonlinear function ƒ by iteration. There is exhibited a family of iterations of order $2\textit{n}-1$ which use $\textit{n}$ evaluations of ƒ and no derivative evaluations, as well as a second family of iterations of order $2\textit{n}-1$ based on $\textit{n}$ — 1 evaluations of ƒ and one of ƒ′. In particular, with four evaluations an iteration of eighth order is constructed. The best previous result for four evaluations was fifth order.It is proved that the $\textit{optimal}$ order of one general class of multipoint iterations is $2\textit{n}-1$ and that an upper bound on the order of a multipoint iteration based on $\textit{n}$ evaluations of ƒ (no derivatives) is $2\textit{n}.It$ is conjectured that a multipoint iteration without memory based on $\textit{n}$ evaluations has optimal order $2\textit{n}-1.$
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1974-10-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 21
Issue Number 4
Page Count 9
Starting Page 643
Ending Page 651


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Source: ACM Digital Library