The Convergence of Multipoint Iterations to Multiple Zeros,

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)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1973
Accession Number
AD0755229

Entities

People

  • G. W. Stewart

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Convergence
  • Iterations
  • Mathematical Analysis

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Systems Analysis and Design