# Accession Number:

## AD0757679

# Title:

## Optimal Order of One-Point and Multipoint Iteration,

# Descriptive Note:

# Corporate Author:

## CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE

# Personal Author(s):

# Report Date:

## 1973-02-01

# Pagination or Media Count:

## 30.0

# Abstract:

The problem is to calculate a simple zero of a non-linear function f by iteration. The authors exhibit a family of iterations of order 2 sup n-1 which use n evaluations of f and no derivative evaluations, as well as a second family of iterations of order 2 sup n-1 based on n-1 evaluations of f and one of f. In particular, with four evaluations, the authors construct an iteration of eighth order. The best previous result for four evaluations was fifth order. It is proven that the optimal order of one general class of multipoint iterations is 2 sup n and that an upper bound on the order of a multipoint iteration based on n evaluations of f no derivatives is 2 sup n. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics