
Accession Number : AD0757679
Title : Optimal Order of OnePoint and Multipoint Iteration,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Kung,H. T. ; Traub,J. F.
Report Date : FEB 1973
Pagination or Media Count : 30
Abstract : The problem is to calculate a simple zero of a nonlinear function f by iteration. The authors exhibit a family of iterations of order 2 sup (n1) which use n evaluations of f and no derivative evaluations, as well as a second family of iterations of order 2 sup (n1) based on n1 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 : (*ITERATIONS, FUNCTIONS(MATHEMATICS)), ALGORITHMS, SET THEORY, POLYNOMIALS, ANALYTIC FUNCTIONS, THEOREMS, OPTIMIZATION
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE