Optimal Order and Efficiency for Iterations with Two Evaluations.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1973
- Accession Number
- AD0787098
Entities
People
- H. T. Kung
- Joseph F. Traub
Organizations
- Carnegie Mellon University