
Accession Number : AD0787098
Title : Optimal Order and Efficiency for Iterations with Two Evaluations.
Descriptive Note : Interim rept.,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Kung,H. T. ; Traub,J. F.
Report Date : NOV 1973
Pagination or Media Count : 32
Abstract : The problem is to calculate a simple zero of a nonlinear function f. The authors consider rational iterations without memory which use two evaluations of f or its derivatives. It is shown that the optimal order is 2. This settles a conjecture of Kung and Traub that an iteration using n evaluations without memory is of order at most 2 sup (n1), for the case n = 2. Furthermore it is shown that any rational twoevaluation iteration of optimal order must use either two evaluations of f or one evaluation of f and one of f'. From this result the authors completely settle the question of the optimal efficiency, in the efficiency measure, for any twoevaluation iteration without memory. (Modified author abstract)
Descriptors : *Rational functions, *Iterations, Analytic functions, Efficiency, Theorems
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE