
Accession Number : AD0755229
Title : The Convergence of Multipoint Iterations to Multiple Zeros,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA DEPT OF MATHEMATICS
Personal Author(s) : Stewart,G. W.
Report Date : JAN 1973
Pagination or Media Count : 27
Abstract : The paper fills a gap in the theory of multipoint iteration function exemplified by the question: how does the secant method converge to a multiple zero. A general theory of the linear convergence of multipoint iterations is developed, and it is shown that two broad classes of iterative methods fit this theory. The results of numerical investigations based on the theory suggest that Muller's method applied to a multiple zero will inevitably produce complex iterates. (Author)
Descriptors : (*MATRICES(MATHEMATICS), ITERATIONS), (*ITERATIONS, CONVERGENCE), COMPLEX VARIABLES, APPROXIMATION(MATHEMATICS), INTERPOLATION, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE