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):

Report Date:

1973-11-01

Pagination or Media Count:

32.0

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

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE