Accession Number : AD0787098

Title :   Optimal Order and Efficiency for Iterations with Two Evaluations.

Descriptive Note : Interim rept.,

Corporate Author : CARNEGIE-MELLON 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 non-linear 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 (n-1), for the case n = 2. Furthermore it is shown that any rational two-evaluation 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 two-evaluation iteration without memory. (Modified author abstract)

Descriptors :   *Rational functions, *Iterations, Analytic functions, Efficiency, Theorems

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE