n-Evaluation Conjecture for Multipoint Iterations for the Solution of Scalar Nonlinear Equations

G. W. Wasilkowski

doi:10.1145/322234.322240

n-Evaluation Conjecture for Multipoint Iterations for the Solution of Scalar Nonlinear Equations

G. W. Wasilkowski

Computer Science

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2 Scopus citations

Abstract

Kung and Traub conjectured that any multipoint iteration without memory which uses n evaluations per iterative step has order of convergence no higher than 2. It is known that this conjecture is true for n --< 3 and for Hermite information. It is proved here that the Kung-Traub conjecture holds in a wider class of iterations. For example, it holds whenever the problem is well poised in the sense of Birkhoff complex interpolation.

Original language	English
Pages (from-to)	71-80
Number of pages	10
Journal	Journal of the ACM (JACM)
Volume	28
Issue number	1
DOIs	https://doi.org/10.1145/322234.322240
State	Published - Jan 1 1981

ASJC Scopus subject areas

Software
Control and Systems Engineering
Information Systems
Hardware and Architecture
Artificial Intelligence

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n-Evaluation Conjecture for Multipoint Iterations for the Solution of Scalar Nonlinear Equations

Abstract

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